GCAXX General California Municipal Money Market Fund (MM)

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C.  20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
INVESTMENT COMPANIES

FORM N-CSR

Item 1.      Reports to Stockholders.

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The views expressed in this report reflect those of the portfolio manager only through the end of the period covered and do not necessarily represent the views of Dreyfus or any other person in the Dreyfus organization. Any such views are subject to change at any time based upon market or other conditions and Dreyfus disclaims any responsibility to update such views.These views may not be relied on as investment advice and, because investment decisions for a Dreyfus fund are based on numerous factors, may not be relied on as an indication of trading intent on behalf of any Dreyfus fund.

Not FDIC-Insured • Not Bank-Guaranteed • May Lose Value

General California
Municipal Money Market Fund

The Fund

A LETTER FROM THE CHAIRMAN AND CEO

Dear Shareholder:

We present to you this semiannual report for General California Municipal Money Market Fund, covering the six-month period from December 1, 2011, through May 31, 2012. For information about how the fund performed during the reporting period, as well as general market perspectives, we provide a Discussion of Fund Performance on the pages that follow.

U.S. financial markets generally rebounded for most of the reporting period before weakening again in the spring of 2012 due to a resurgent sovereign debt crisis in Europe and disappointing economic data in the United States.These developments created a “risk-on/risk-off” investment climate in which market sentiment shifted rapidly between optimism and caution. In contrast, yields of money market instruments remained stable near historical lows, as an aggressively accommodative monetary policy from the Federal Reserve Board prevented yields from rising or falling appreciably in light of changing economic news.

Despite recently troubling headlines, we believe that U.S. economic trends remain favorable, as evidenced by signs of strength in some of the domestic economy’s more economically sensitive areas. On the other hand, net exports may prove to be a slight drag on domestic growth since the economy in the United States is stronger than in many of its trading partners. On the whole, we expect near-trend growth in the U.S. economy for the remainder of 2012.

As always, we encourage you to discuss our observations with your financial advisor.

Thank you for your continued confidence and support.

Jonathan R. Baum
Chairman and Chief Executive Officer
The Dreyfus Corporation
June 15, 2012

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DISCUSSION OF FUND PERFORMANCE

For the period of December 1, 2011, through May 31, 2012, as provided by Joseph Irace, Senior Portfolio Manager

Fund and Market Performance Overview

For the six-month period ended May 31, 2012, General California Municipal Money Market Fund’s Class A and Class B shares produced annualized yields of 0.00% and 0.00%, respectively.Taking into account the effects of compounding, the fund’s Class A and Class B shares produced annualized effective yields of 0.00% and 0.00%, respectively. ¹

The U.S. economic recovery proved erratic during the reporting period, but yields of tax-exempt money market instruments remained stable near zero percent as the Federal Reserve Board (the “Fed”) left short-term interest rates unchanged at historically low levels.

The Fund’s Investment Approach

The fund seeks to maximize current income exempt from federal and California state personal income taxes to the extent consistent with the preservation of capital and the maintenance of liquidity.To pursue its goal, the fund normally invests substantially all of its net assets in short-term, high quality municipal obligations that provide income exempt from federal and California state income taxes. The fund may also invest in high quality, short-term structured notes, which are derivative instruments whose value is tied to underlying municipal obligations.

In pursuing this objective, we employ two primary strategies. First, we normally attempt to add value by constructing a portfolio of high-quality, municipal money market instruments that provide income exempt from federal and California state personal income taxes. Second, we actively manage the fund’s average maturity based on our anticipation of supply-and-demand changes in California’s short-term municipal marketplace.

For example, if we expect an increase in short-term supply, we may decrease the average maturity of the fund, which could enable us to take advantage of opportunities when short-term supply increases.

DISCUSSION OF FUND PERFORMANCE (continued)

Generally, yields tend to rise when there is an increase in new-issue supply competing for investor interest. New securities, which are generally issued with maturities in the one-year range, may in turn lengthen the fund’s weighted average maturity if purchased. If we anticipate limited new-issue supply, we may then look to extend the fund’s average maturity to maintain then-current yields for as long as we believe practical. In addition, we try to maintain an average maturity that reflects our view of short-term interest-rate trends and future supply-and-demand considerations.

Economic Sentiment Shifted, but Yields Remained Low

Most U.S. financial markets were in the midst of a rally at the start of the reporting period, as investors responded positively to U.S. employment gains and what seemed to be credible measures by European poli-cymakers to address the region’s sovereign debt crisis. However, new developments in the spring of 2012 called the sustainability of these positive influences into question.The U.S. labor market’s rebound slowed as the public sector shed jobs and the private sector’s employment gains proved more anemic than expected. Austerity measures designed to relieve fiscal pressures in Europe encountered resistance in some countries, threatening proposed bailouts and the region’s economic prospects.

Despite the changing economic outlook, the Fed maintained the policy stance it first established in December 2008, leaving the overnight federal funds rate in a range between 0% and 0.25%, and municipal money market yields remained near zero percent.

Demand for municipal money market instruments proved robust during the reporting period. Narrow yield differences along the market’s maturity range and attractive after-tax yields compared to taxable money market instruments attracted individual investors as well as institutions that typically participate in taxable and longer-term bond markets. Consequently, yields of variable-rate demand notes (VRDNs) remained in a relatively narrow trading range. Meanwhile, the supply of newly issued tax-exempt money market instruments remained relatively steady as highly rated banks filled a gap left by struggling European financial institutions in issuing the letters of credit that typically backVRDNs.

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From a credit-quality perspective, California has continued to struggle with large budget deficits and disappointing tax revenues.Although the state has made some progress in shoring up its fiscal condition, a recent court ruling could weaken prospects for further improvement.

A Credit-Conscious Investment Posture

We continued to maintain a careful and well-researched approach to credit selection, focusing on essential service revenue bonds issued by water, sewer and electric enterprises, and certain local credits from issuers with strong financial positions and stable tax bases.We generally shied away from instruments issued by localities that depend heavily on state aid, and we maintained the fund’s weighted average maturity in a range that was roughly in line with industry averages.

Outlook Clouded by Economic Uncertainty

We are cautiously optimistic regarding the prospects for economic growth over the remainder of 2012. Strains in global financial markets have continued to pose significant challenges, but the Fed expects a moderate pace of economic growth and a gradually declining unemployment rate. In addition, the Fed has signaled repeatedly that it is prepared to maintain short-term interest rates near current levels through late 2014. With money market yields likely to remain near historical lows for some time to come, we believe that the prudent course continues to be an emphasis on preservation of capital and liquidity.

June 15, 2012

UNDERSTANDING YOUR FUND’S EXPENSES (Unaudited)

As a mutual fund investor, you pay ongoing expenses, such as management fees and other expenses. Using the information below, you can estimate how these expenses affect your investment and compare them with the expenses of other funds.You also may pay one-time transaction expenses, including sales charges (loads) and redemption fees, which are not shown in this section and would have resulted in higher total expenses. For more information, see your fund’s prospectus or talk to your financial adviser.

Review your fund’s expenses

The table below shows the expenses you would have paid on a $1,000 investment in General California Municipal Money Market Fund from December 1, 2011 to May 31, 2012. It also shows how much a $1,000 investment would be worth at the close of the period, assuming actual returns and expenses.

Using the SEC’s method to compare expenses

The Securities and Exchange Commission (SEC) has established guidelines to help investors assess fund expenses. Per these guidelines, the table below shows your fund’s expenses based on a $1,000 investment, assuming a hypothetical 5% annualized return. You can use this information to compare the ongoing expenses (but not transaction expenses or total cost) of investing in the fund with those of other funds.All mutual fund shareholder reports will provide this information to help you make this comparison. Please note that you cannot use this information to estimate your actual ending account balance and expenses paid during the period.

† Expenses are equal to the fund’s annualized expense ratio of .26% for Class A shares and .26% for Class B shares, multiplied by the average account value over the period, multiplied by 183/366 (to reflect the one-half year period).

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STATEMENT OF INVESTMENTS (Unaudited) (continued)

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STATEMENT OF INVESTMENTS (Unaudited) (continued)

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STATEMENT OF INVESTMENTS (Unaudited) (continued)

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STATEMENT OF INVESTMENTS (Unaudited) (continued)

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STATEMENT OF INVESTMENTS (Unaudited) (continued)

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STATEMENT OF CHANGES IN NET ASSETS

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FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the fiscal periods indicated. All information reflects financial results for a single fund share. Total return shows how much your investment in the fund would have increased (or decreased) during each period, assuming you had reinvested all dividends and distributions.These figures have been derived from the fund’s financial statements.

FINANCIAL HIGHLIGHTS (continued)

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NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1—Significant Accounting Policies:

General California Municipal Money Market Fund (the “fund”) is registered under the Investment Company Act of 1940, as amended (the “Act”), as a non-diversified open-end management investment company. The fund’s investment objective is to maximize current income exempt from federal and California state income taxes, to the extent consistent with the preservation of capital and the maintenance of liquidity. The Dreyfus Corporation (the “Manager” or “Dreyfus”), a wholly-owned subsidiary of The Bank of New York Mellon Corporation (“BNY Mellon”), serves as the fund’s investment adviser.

MBSC Securities Corporation (the “Distributor”), a wholly-owned subsidiary of the Manager, is the distributor of the fund’s shares. The fund is authorized to issue an unlimited number of $.001 par value shares of Beneficial Interest in the following classes of shares: Class A and Class B. Class A and Class B shares are identical except for the services offered to and the expenses borne by each class, the allocation of certain transfer agency costs and certain voting rights. Class B shares are subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act and Class A and Class B shares are subject to a Shareholder Services Plan. In addition, Class B shares are charged directly for sub-accounting services provided by Service Agents (a securities dealer, financial institution or other industry professional) at an annual rate of .05% of the value of the average daily net assets of Class B shares. During the period ended May 31, 2012, sub-accounting service fees amounted to $14,232, for Class B shares and are included in Shareholder servicing costs in the Statement of Operations. Income, expenses (other than expenses attributable to a specific class), and

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

realized and unrealized gains or losses on investments are allocated to each class of shares based on its relative net assets.

It is the fund’s policy to maintain a continuous net asset value per share of $1.00; the fund has adopted certain investment, portfolio valuation and dividend and distribution policies to enable it to do so.There is no assurance, however, that the fund will be able to maintain a stable net asset value per share of $1.00.

The Financial Accounting Standards Board (“FASB”) Accounting Standards Codification is the exclusive reference of authoritative U.S. generally accepted accounting principles (“GAAP”) recognized by the FASB to be applied by nongovernmental entities. Rules and interpretive releases of the Securities and Exchange Commission (“SEC”) under authority of federal laws are also sources of authoritative GAAP for SEC registrants. The fund’s financial statements are prepared in accordance with GAAP, which may require the use of management estimates and assumptions.Actual results could differ from those estimates.

The fund enters into contracts that contain a variety of indemnifications. The fund’s maximum exposure under these arrangements is unknown.The fund does not anticipate recognizing any loss related to these arrangements.

(a) Portfolio valuation: Investments in securities are valued at amortized cost in accordance with Rule 2a-7 of the Act, which has been determined by the Board of Trustees to represent the fair value of the fund’s investments.

The fair value of a financial instrument is the amount that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date (i.e., the exit price). GAAP establishes a fair value hierarchy that prioritizes the inputs of valuation techniques used to measure fair value.This hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets or liabilities (Level 1 measurements) and the lowest priority to unobservable inputs (Level 3 measurements).

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Additionally, GAAP provides guidance on determining whether the volume and activity in a market has decreased significantly and whether such a decrease in activity results in transactions that are not orderly. GAAP requires enhanced disclosures around valuation inputs and techniques used during annual and interim periods.

Various inputs are used in determining the value of the fund’s investments relating to fair value measurements.These inputs are summarized in the three broad levels listed below:

Level 1 —unadjusted quoted prices in active markets for identical investments.

Level 2 —other significant observable inputs (including quoted prices for similar investments, interest rates, prepayment speeds, credit risk, etc.).

Level 3 —significant unobservable inputs (including the fund’s own assumptions in determining the fair value of investments).

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities. For example, money market securities are valued using amortized cost, in accordance with rules under the Act. Generally, amortized cost approximates the current fair value of a security, but since the value is not obtained from a quoted price in an active market, such securities are reflected within Level 2 of the fair value hierarchy.

The following is a summary of the inputs used as of May 31, 2012 in valuing the fund’s investments:

† See Statement of Investments for additional detailed categorizations.

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

In May 2011, FASB issued Accounting Standards Update (“ASU”) No. 2011-04 “Amendments to Achieve Common FairValue Measurement and Disclosure Requirements in GAAP and International Financial Reporting Standards (“IFRS”)” (“ASU 2011-04”). ASU 2011-04 includes common requirements for measurement of and disclosure about fair value between GAAP and IFRS. ASU 2011-04 will require reporting entities to disclose the following information for fair value measurements categorized within Level 3 of the fair value hierarchy: quantitative information about the unobservable inputs used in the fair value measurement, the valuation processes used by the reporting entity and a narrative description of the sensitivity of the fair value measurement to changes in unobservable inputs and the interrelationships between those unobservable inputs. In addition, ASU 2011-04 will require reporting entities to make disclosures about amounts and reasons for all transfers in and out of Level 1 and Level 2 fair value measurements.The new and revised disclosures are effective for interim and annual reporting periods beginning after December 15, 2011. At this time, management is evaluating the implications of ASU 2011-04 and its impact on the financial statements.

(b) Securities transactions and investment income: Securities transactions are recorded on a trade date basis. Interest income, adjusted for accretion of discount and amortization of premium on investments, is earned from settlement date and is recognized on the accrual basis. Realized gains and losses from securities transactions are recorded on the identified cost basis. Cost of investments represents amortized cost.

The fund follows an investment policy of investing primarily in municipal obligations of one state. Economic changes affecting the state and certain of its public bodies and municipalities may affect the ability of issuers within the state to pay interest on, or repay principal of, municipal obligations held by the fund.

(c) Dividends to shareholders: It is the policy of the fund to declare dividends daily from investment income-net. Such dividends are paid monthly. Dividends from net realized capital gains, if any, are normally

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declared and paid annually, but the fund may make distributions on a more frequent basis to comply with the distribution requirements of the Internal Revenue Code of 1986, as amended (the “Code”).To the extent that net realized capital gains can be offset by capital loss carryovers, it is the policy of the fund not to distribute such gains.

(d) Federal income taxes: It is the policy of the fund to continue to qualify as a regulated investment company, which can distribute tax exempt dividends, by complying with the applicable provisions of the Code, and to make distributions of income and net realized capital gain sufficient to relieve it from substantially all federal income and excise taxes.

As of and during the period ended May 31, 2012, the fund did not have any liabilities for any uncertain tax positions.The fund recognizes interest and penalties, if any, related to uncertain tax positions as income tax expense in the Statement of Operations. During the period, the fund did not incur any interest or penalties.

Each of the tax years in the three-year period ended November 30, 2011 remains subject to examination by the Internal Revenue Service and state taxing authorities.

The tax character of distributions paid to shareholders during the fiscal year ended November 30, 2011 was as follows: tax exempt income $78 and ordinary income $416.The tax character of current year distributions will be determined at the end of the current fiscal year.

At May 31, 2012, the cost of investments for federal income tax purposes was substantially the same as the cost for financial reporting purposes (See the Statement of Investments).

NOTE 2—Management Fee and Other Transactions With Affiliates:

(a) Pursuant to a management agreement (“Agreement”) with the Manager, the management fee is computed at the annual rate of .50% of the value of the fund’s average daily net assets and is payable monthly.

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

The Agreement provides that if in any full fiscal year the aggregate expenses, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed 1 ¹ / ₂ % of the value of the fund’s average daily net assets, the fund may deduct from payments to be made to the Manager, or the Manager will bear such excess expense. During the period ended May 31, 2012, there was no expense reimbursement pursuant to the Agreement.

The Manager has undertaken to waive receipt of the management fee and/or reimburse operating expenses in order to facilitate a daily yield at or above a certain level which may change from time to time.This undertaking is voluntary and not contractual, and may be terminated at any time. The reduction in expenses, pursuant to the undertaking amounted to $530,174 for Class A and $211,788 for Class B shares during the period ended May 31, 2012.

(b) Under the Distribution Plan with respect to Class B (“Distribution Plan”), adopted pursuant to Rule 12b-1 under the Act, Class B shares bear directly the cost of preparing, printing and distributing prospectuses and statements of additional information and of implementing and operating the Distribution Plan, such aggregate amount not to exceed in any fiscal year of the fund, the greater of $100,000 or .005% of the average daily net assets of Class B shares. In addition, Class B shares reimburse the Distributor for payments made to third parties for distributing Class B shares at an annual rate not to exceed .20% of the value of the average daily net assets of Class B shares. During the period ended May 31, 2012, Class B shares were charged $58,441 pursuant to the Distribution Plan.

(c) Under the Shareholder Services Plan with respect to Class A (“Class A Shareholder Services Plan”),Class A shares reimburse the Distributor an amount not to exceed an annual rate of .25% of the value of the average daily net assets of Class A shares for certain allocated expenses of providing personal services and/or maintaining shareholder accounts.The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries

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regarding Class A shares and providing reports and other information, and services related to the maintenance of shareholder accounts. During the period ended May 31, 2012, Class A shares were charged $45,600 pursuant to the Class A Shareholder Services Plan.

Under the Shareholder Services Plan with respect to Class B (“Class B Shareholder Services Plan”), Class B shares pay the Distributor at an annual rate of .25% of the value of the average daily net assets of Class B shares for servicing shareholder accounts. The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries regarding Class B shares and providing reports and other information, and services related to the maintenance of shareholder accounts.The Distributor may make payments to Service Agents in respect of their services. The Distributor determines the amounts to be paid to Service Agents.

The Manager had undertaken from December 1, 2011 through May 31, 2012 to reduce the expenses of Class B shares, if the aggregate expenses of Class B shares, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceeded an annual rate of 1% of the value of the average daily net assets of Class B shares. Such expense limitations are voluntary, temporary and may be revised or terminated at any time. During the period ended May 31, 2012, Class B shares were charged $71,162 pursuant to the Class B Shareholder Services Plan, of which $21,911 was reimbursed by the Manager.

The fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the Manager, under a transfer agency and cash management agreement for providing personnel and facilities to perform transfer agency services for the fund. During the period ended May 31, 2012, the fund was charged $19,808 pursuant to the transfer agency agreement, which is included in Shareholder servicing costs in the Statement of Operations.

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

The fund compensates The Bank of NewYork Mellon under a custody agreement for providing custodial services for the fund. During the period ended May 31, 2012, the fund was charged $18,188 pursuant to the custody agreement.

The fund has arrangements with the transfer agent and the custodian whereby the fund may receive earnings credits when positive cash balances are maintained, which are used to offset transfer agency and custody fees. For financial reporting purposes, the fund includes net earnings credits as an expense offset in the Statement of Operations.

Prior to May 29, 2012, the fund compensated The Bank of NewYork Mellon, a subsidiary of BNY Mellon and an affiliate of Dreyfus, under a cash management agreement for performing cash management services related to fund subscriptions and redemptions. During the period ended May 31, 2012, the fund was charged $1,664 pursuant to the cash management agreement, which is included in Shareholder servicing costs in the Statement of Operations. These fees were partially offset by earnings credits of $69.

During the period ended May 31, 2012, the fund was charged $3,183 for services performed by the Chief Compliance Officer and his staff.

The components of “Due to The Dreyfus Corporation and affiliates” in the Statement of Assets and Liabilities consist of: management fees $139,424, Rule 12b-1 distribution plan fees $9,818, shareholder services plan fees $14,727, custodian fees $9,234, chief compliance officer fees $2,652 and transfer agency per account fees $9,714, which are offset against an expense reimbursement currently in effect in the amount of $117,359.

(d) Each Board member also serves as a Board member of other funds within the Dreyfus complex. Annual retainer fees and attendance fees are allocated to each fund based on net assets.

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NOTE 3—Securities Transactions:

The fund is permitted to purchase or sell securities from or to certain affiliated funds under specified conditions outlined in procedures adopted by the Board ofTrustees.The procedures have been designed to ensure that any purchase or sale of securities by the fund from or to another fund or portfolio that are, or could be, considered an affiliate by virtue of having a common investment adviser (or affiliated investment adviser), common Trustees and/or common officers, complies with Rule 17a-7 of the Act. During the period ended May 31, 2012, the fund engaged in purchases and sales of securities pursuant to Rule 17a-7 of the Act amounting to $171,540,000 and $83,700,000, respectively.

NOTES

Item 2.      Code of Ethics.

                  Not applicable.

Item 3.      Audit Committee Financial Expert.

                  Not applicable.

Item 4.      Principal Accountant Fees and Services.

                  Not applicable.

Item 5.      Audit Committee of Listed Registrants.

                  Not applicable.

Item 6.      Investments.

(a)              Not applicable.

Item 7.      Disclosure of Proxy Voting Policies and Procedures for Closed-End Management      Investment Companies.

                  Not applicable.

Item 8.      Portfolio Managers of Closed-End Management Investment Companies.

Not applicable.

Item 9.      Purchases of Equity Securities by Closed-End Management Investment Companies and        Affiliated Purchasers.

                  Not applicable.  [CLOSED END FUNDS ONLY]

Item 10.    Submission of Matters to a Vote of Security Holders.

                  There have been no material changes to the procedures applicable to Item 10.

Item 11.    Controls and Procedures.

(a)        The Registrant's principal executive and principal financial officers have concluded, based on their evaluation of the Registrant's disclosure controls and procedures as of a date within 90 days of the filing date of this report, that the Registrant's disclosure controls and procedures are reasonably designed to ensure that information required to be disclosed by the Registrant on Form N-CSR is recorded, processed, summarized and reported within the required time periods and that information required to be disclosed by the Registrant in the reports that it files or submits on Form N-CSR is accumulated and communicated to the Registrant's management, including its principal executive and principal financial officers, as appropriate to allow timely decisions regarding required disclosure.

(b)        There were no changes to the Registrant's internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that have materially affected, or are reasonably likely to materially affect, the Registrant's internal control over financial reporting.

Item 12.    Exhibits.

(a)(1)   Not applicable.

(a)(2)   Certifications of principal executive and principal financial officers as required by Rule 30a-2(a) under the Investment Company Act of 1940.

(a)(3)   Not applicable.

(b)        Certification of principal executive and principal financial officers as required by Rule 30a-2(b) under the Investment Company Act of 1940.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the Registrant has duly caused this Report to be signed on its behalf by the undersigned, thereunto duly authorized.

General California Municipal Money Market Fund

EXHIBIT INDEX

(a)(2)   Certifications of principal executive and principal financial officers as required by Rule 30a-2(a) under the Investment Company Act of 1940.  (EX-99.CERT)

(b)        Certification of principal executive and principal financial officers as required by Rule 30a-2(b) under the Investment Company Act of 1940.  (EX-99.906CERT)