GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1995-03-28
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this semi-annual report for the
General California Municipal Money Market Fund. For the period ended January
31, 1995, the annualized yield provided by your Fund was 2.96%. The
annualized effective yield was 3.00% after taking into account the effect of
compounding.* Income dividends of approximately $.015 per share paid during
the period were exempt from Federal and State of California personal income
taxes.**
    Our last letter recapped the series of Federal Reserve Board moves
throughout the first half of 1994 -- moves designed to reach a more neutral
monetary policy stance in response to continued economic expansion. With
further evidence of economic strength in the latter half of the year, the
Federal Reserve Board continued its move toward tighter policy. In two
successive moves in August and November, the Fed increased rates an
additional 125 basis points. By November 15, total monetary policy actions
taken in 1994 increased the discount rate from 3.00% to 4.75%. In addition,
the Federal Funds rate moved from 3.00% to 5.50% between February and
November of last year. On February 1 of this year, the Fed continued with its
policy as it raised both the Federal Funds and discount rates an additional
50 basis points to 6.00% and 5.25%, respectively. Throughout the year, yields
on municipal money market funds increased in response to these higher
short-term rates.
    The bankruptcy filing by Orange County, California, which occurred in the
second half of last year, was one of the most significant events to affect
the short-term municipal market. The uncertainty that resulted caused
temporary market weakness in both the national and state-specific money
markets. Your Fund had no direct exposure to Orange County; however, prices
on short-term municipal notes (especially California issues) declined as the
market awaited additional information about the County's filing. The
prevailing market weakness provided several attractive buying opportunities
in the California market. However, in accordance with our conservative
portfolio strategy and our awareness of shareholder concern, we invested any
available cash in the short end of our market. As market conditions allow, we
will selectively seek out high-quality California-exempt issues that provide
the portfolio with a high level of diversity and liquidity.
    We have provided a current Statement of Investments and recent financial
statements for your review and look forward to serving your investment needs
in the future.
                              Very truly yours,
                              (logo signature)
                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
February 15, 1995
New York, N.Y.

  *    Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
**Some income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.

<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                          JANUARY 31, 1995 (UNAUDITED)
                                                                                          PRINCIPAL
TAX EXEMPT INVESTMENTS--100.0%                                                              AMOUNT           VALUE
                                                                                        --------------    --------------
<S>                                                                                       <C>            <C>
Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)
    2.80% (LOC; National Bank of Canada) (a,b)..............................              $  8,850,000   $ 8,850,000
State of California, RAN 5%, Series A, 6/28/95..............................                 5,000,000     5,020,603
California Health Facilities Authority, Multi-Family Revenue, Refunding, VRDN
    (Scripps Memorial Hospital) 3.70%, Series B
    (Insured; MBIA and Liquidity Facility; Morgan Guaranty Trust Co.) (a)...                17,700,000    17,700,000
California Housing Finance Agency:
    Home Mortgage Revenue 4.30%, Series F-3, 10/2/95 (GIC; Goldman, Sachs)..                  9,000,000    9,000,000
    Multi-Family Revenue, Refunding, VRDN:
      3.40%, Series B (Corp. Guaranty; Federal National Mortgage Association) (a)             5,600,000    5,600,000
      3.40%, Series C (Corp. Guaranty; Federal National Mortgage Association) (a)             5,400,000    5,400,000
California Pollution Control Financing Authority, VRDN:
    (Colmac Energy Project) 3.40%, Series A (LOC; Swiss Bank Corp.) (a,b)...                  6,500,000    6,500,000
    RRR:
      (Atlantic Richfield Co. Project) 3.90%, Series A (Corp. Guaranty; Arco) (a)            19,400,000   19,400,000
      (Delano Project) 4.10% (LOC; ABN-Amro Bank) (a,b).....................                 32,700,000   32,700,000
      (Honey Lake Power Co. Project) 4.10% (LOC; Banque Nationale de Paris) (a,b)             9,500,000    9,500,000
      Refunding:
          (Ultra Power Malaga Project) 4.15%, Series B (LOC; Bank of America) (a,b)           2,800,000    2,800,000
          (Ultra Power Rocklin Project) 4.15%, Series A (LOC; Bank of America) (a,b)         16,400,000   16,400,000
          (Ultra Power Rocklin Project) 4.15%, Series B (LOC; Bank of America) (a,b)          3,900,000    3,900,000
California School Cash Reserve Program Authority, Notes 4.50%, Series A, 7/5/95              11,000,000   11,033,509
California Statewide Community Development Authority, Revenue, TRAN
    4.50%, Series A, 7/17/95................................................                 23,000,000   23,077,093
California Statewide Community Development Authority, Solid Waste Facilities
Revenue
    VRDN (Chevron USA Inc. Project) 3.85%, (Corp. Guaranty; Chevron USA Inc.) (a)             7,700,000    7,700,000
City of Camarillo, MFHR, VRDN (Heritage Park) 3.50%, Series A
    (Corp. Guaranty; Federal National Mortgage Association) (a).............                  7,100,000    7,100,000
Garden Grove Housing Authority, Multi-Family Revenue, VRDN
    (Valley View Senior Villas Project) 4.30%, Series A (LOC; Wells Fargo Bank) (a,b)         1,600,000    1,600,000
Huntington Beach, MFHR, VRDN:
    (Five Points Seniors Project) 4.30%, Series A (LOC; Wells Fargo Bank) (a,b)               3,100,000    3,100,000
    (Mercury Savings and Loan Village) 4%, Series A
      (LOC; Resoultion Funding Corp.) (a,b).................................                  6,000,000    6,000,000
Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.75% (LOC; Bankers Trust) (a,b)              3,000,000    3,000,000
Los Angeles, MFHR, VRDN:
    4.20%, Series B (LOC; Federal Home Loan Banks) (a,b)....................                  7,500,000    7,500,000
    (Beverly Park Apartments) 3.60%, Series A (LOC; Barclays Bank) (a,b)....                  9,600,000    9,600,000
    (Lucas Studios Project) 3.90%, Series D (LOC; Bank of America) (a,b)....                  3,765,000    3,765,000
    (Oakwood Apartments) 4.05%, Series B (LOC; Sumitomo Bank) (a,b).........                  9,695,000    9,695,000
    (Studio Colony) 3.25%, Series C (LOC; Industrial Bank of Japan) (a,b)...                  9,795,000    9,795,000
Los Angeles Community Redevelopment Agency, MFHR, VRDN
    (Rental Academy Apartments) 3.80%, Series A (LOC; Dai-Ichi Kangyo Bank) (a,b)             6,300,000    6,300,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)              JANUARY 31, 1995 (UNAUDITED)
                                                                                         PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                          AMOUNT           VALUE
                                                                                        --------------    --------------
Los Angeles County, TRAN 4.50%, 6/30/95.....................................             $  13,710,000    $  13,745,019
Los Angeles County Housing Authority, MFHR, VRDN
    (River Park Apartment Project) 3.70%, Series D (LOC; Dai-Ichi Kangyo Bank) (a,b)         5,000,000        5,000,000
Los Angeles County Local Educational Agencies, COP, TRAN 4.50%, 7/6/95......                 8,000,000        8,024,528
Los Angeles County Metropolitan Transportation Authority:
    Revenue, RAN 3.75%, Series A, 3/14/95 (LOC; Union Bank of Switzerland) (b)              14,000,000       14,006,844
    Sales Tax Revenue, Refunding, VRDN (Property C) 3.50%, Series A
      (Insured; MBIA, SBPA; Industrial Bank of Japan) (a)...................                23,200,000       23,200,000
Los Angeles Unified School District, TRAN 4.50%, 7/10/95....................                10,875,000       10,916,125
Paramount, MFHR, VRDN (Mercury Savings and Loan Triangle Project)
    4%, Series A (LOC; Resolution Funding Corp.) (a,b)......................                  9,000,000       9,000,000
City of Richmond, VRDN 4% (BPA; Societe Generale) (a).......................                  5,000,000       5,000,000
Riverside County, TRAN 4.25%, 6/30/95.......................................                 10,000,000      10,025,584
Riverside County Housing Authority, VRDN, MFHR
    (Victoria Springs Apartments) 4.10% (LOC; Bank of America) (a,b)........                  6,300,000       6,300,000
Riverside County School Financing Authority, RAN (School District Financing)
    4.50%, 7/7/95...........................................................                 23,100,000      23,180,909
Sacramento County, MFHR, VRDN
    3.70%, Series C (LOC; Dai-Ichi Kangyo Bank) (a,b).......................                  2,400,000       2,400,000
Sacramento County Housing Authority, MFHR, VRDN (Stone Creek Apartments
Project)
    3.75%, Series L (LOC; First Interstate Bank of California) (a,b)........                  5,450,000       5,450,000
San Bernardino, COP, VRDN 3.89% (LOC; Sumitomo Trust and Banking Co.) (a,b).                 12,000,000      12,000,000
San Bernardino Board of Education, TRAN 4.25%, 7/28/95......................                 10,000,000      10,013,492
San Bernardino County, MFHR, VRDN (Meadowland Apartments Project)
    3.95%, Series A (LOC; Bayerische Landesbank Girozentrale) (a,b).........                  7,860,000       7,860,000
San Diego Area Local Government, COP, TRAN 4.50%, 6/30/95...................                 15,000,000      15,051,610
San Diego County Regional Transportation Commission, Sales Tax Revenue, VRDN
    3.60%, (Insured; FGIC) (a)..............................................                  6,000,000       6,000,000
San Diego Housing Authority, MFHR, VRDN (Nobel Court Apartments)
    3.60% (LOC; Citibank) (a,b).............................................                  4,000,000       4,000,000
San Diego MFHR, VRDN:
    (Country Hills Apartments) 3.40%, Series A
      (Corp. Guaranty; Federal National Mortgage Association) (a)...........                  5,400,000      5,400,000
    Refunding (Univeristy Town Center Apartments)
      3.55% (LOC; Bank of America) (a,b)....................................                  7,000,000      7,000,000
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
    (French Co. Project) 3.90% (LOC; Credit Commercial de France) (a,b).....                  4,600,000      4,600,000
San Francisco City and County Redevelopment Agency, Multi-Family Revenue,
VRDN
    (Bayside Village Project) 3.525%, Series A (LOC; Industrial Bank of Japan) (a,b)          6,000,000       6,000,000
Simi Valley, MFHR, Refunding, VRDN 3.25%, Series A (LOC; Bank of America) (a,b)              11,970,000      11,970,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)             JANUARY 31, 1995 (UNAUDITED)
                                                                                          PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                          AMOUNT           VALUE
                                                                                        --------------    --------------
Southern California Public Power Authority, Transmission Project Revenue,
Refunding
    VRDN (Southern Transmission) 3.25% (Insured; AMBAC and LOC; Swiss Bank
Corp.) (a,b)....................................................        $  15,000,000$  15,000,000
Vacaville, MFMR, VRDN (Quail Run) 3.40%, Series A
    (Corp. Guaranty; Federal National Mortgage Association) (a,b)...........                  3,000,000    3,000,000
                                                                                                        --------------
TOTAL INVESTMENTS (cost $496,180,316).......................................                           $496,180,316
                                                                                                        --------------
                                                                                                        --------------
</TABLE>
<TABLE>
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <C>     <C>
AMBAC         American Municipal Bond Assurance Corporation      MFHR    Multi-Family Housing Revenue
BPA           Bond Purchase Agreement                            MFMR    Multi-Family Mortgage Revenue
COP           Certificate of Participation                       RAN     Revenue Anticipation Notes
FGIC          Financial Guaranty Insurance Company               RRR     Resources Recovery Revenue
GIC           Guaranty Investment Contract                       SBPA    Standby Bond Purchase Agreement
IDR           Industrial Development Revenue                     TRAN    Tax and Revenue Anticipation Notes
LOC           Letter of Credit                                   VRDN    Variable Rate Demand Notes
MBIA          Municipal Bond Investors Assurance

</TABLE>
<TABLE>
SUMMARY OF COMBINED RATINGS
MOODY'S                             OR                STANDARD & POOR'S                      PERCENTAGE OF VALUE
- ---------                                             --------------------                  ----------------------
<S>                                                   <C>                                           <C>
VMIG1/MIG1, P1 (c)                                    SP1+/SP1, A1+/A1 (c)                          90.6%
Aaa/Aa (d)                                            AAA/AA (d)                                     3.0
Not Rated (e)                                         Not Rated (e)                                  6.4
                                                                                                   --------
                                                                                                    100.0%
                                                                                                   =======
</TABLE>


NOTES TO STATEMENT OF INVESTMENT:
    (a)  Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index of market interest
    rates.
    (b)  Secured by letters of credit. At January 31, 1995, 49.4% of the
    Fund's net assets are backed by letters of credit issued by domestic
    banks and foriegn banks, of which 10.2% was provided by Bank of America.
    (c)  P1 and A1 are the highest ratings assigned tax-exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (d)  Notes which are not MIG or SP rated are represented by bond ratings
    of the issuers.
    (e)  Securities which, while not rated by Moody's and Standard & Poor's,
    respectively, have been determined by the Fund's Board of Trustees to be
    of comparable quality to those rated securities in which the Fund may
    invest.
    (f)  At January 31, 1995, the Fund had $166,685,000 (32.7% of net assets)
    invested in securities whose payment of prinicipal and interest is
    dependent upon revenues generated from housing projects.






See independent accountants' review report and notes to financial statements.
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES               JANUARY 31, 1995 (UNAUDITED)
<S>                                                                                           <C>         <C>
ASSETS:
    Investments in securities, at value_Note 1(a)...........................                              $496,180,316
    Cash....................................................................                                 4,370,854
    Interest receivable.....................................................                                 4,997,634
    Receivable for investment securities sold...............................                                 4,001,775
    Prepaid expenses........................................................                                    46,943
                                                                                                        --------------
                                                                                                           509,597,522
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                  $204,219
    Accrued expenses and other liabilities..................................                   127,203         331,422
                                                                                            ----------    -------------
NET ASSETS  ................................................................                               $509,266,100
                                                                                                          =============
REPRESENTED BY:
    Paid-in capital.........................................................                               $509,388,079
    Accumulated net realized (loss) on investments..........................                                  (121,979)
                                                                                                         --------------
NET ASSETS at value applicable to 509,388,079 outstanding shares of
    Beneficial Interest, equivalent to $1.00 per share (unlimited number of
    $.001 par value shares authorized)......................................                               $509,266,100
                                                                                                          =============






See independent accountants' review report and notes to financial statements.
</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS          SIX MONTHS ENDED JANUARY 31, 1995 (UNAUDITED)
<S>                                                                                        <C>           <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                             $10,493,092
    EXPENSES:
      Management fee_Note 2(a)..............................................                $1,543,778
      Shareholder servicing costs_Note 2(b).................................                   259,555
      Custodian fees........................................................                    29,610
      Professional fees.....................................................                    18,483
      Prospectus and shareholders' reports..................................                    13,659
      Trustees' fees and expenses_Note 2(c).................................                     8,928
      Registration fees.....................................................                     4,519
      Miscellaneous.........................................................                    11,060
                                                                                          ------------
                                                                                             1,889,592
      Less_reduction in management fee due to
          undertakings_Note 2(a)............................................                   467,104
                                                                                          ------------
            TOTAL EXPENSES..................................................                                  1,422,488
                                                                                                          -------------
INVESTMENT INCOME--NET......................................................                                  9,070,604
NET REALIZED (LOSS) ON INVESTMENTS..........................................                                    (2,323)
                                                                                                          -------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                               $  9,068,281
                                                                                                           ============



See independent accountants' review report and notes to financial statements.
</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                     YEAR ENDED    SIX MONTHS ENDED
                                                                                      JULY 31,      JANUARY 31, 1995
                                                                                        1994           (UNAUDITED)
                                                                                  ----------------    ---------------
<S>                                                                               <C>                  <C>
OPERATIONS:
    Investment income_net.............................................            $     15,589,793     $    9,070,604
    Net realized (loss) on investments................................                   (111,389)            (2,323)
                                                                                  ----------------    ----------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS............                 15,478,404            9,068,281
                                                                                  ----------------    ----------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income_net.............................................                (15,589,793)        (9,070,604)
                                                                                  ----------------    ----------------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold.....................................              2,518,641,419          909,661,104
    Dividends reinvested..............................................                 14,582,815            8,318,348
    Cost of shares redeemed...........................................            (2,442,541,575)      (1,107,816,008)
                                                                                  ----------------    ----------------
      INCREASE (DECREASE) IN NET ASSETS FROM BENEFICIAL INTEREST
          TRANSACTIONS................................................                 90,682,659        (189,836,556)
                                                                                  ----------------    ----------------
          TOTAL INCREASE (DECREASE) IN NET ASSETS.....................                 90,571,270        (189,838,879)
NET ASSETS:
    Beginning of period...............................................                608,533,709          699,104,979
                                                                                  ----------------    ----------------
    End of period.....................................................            $   699,104,979      $   509,266,100
                                                                                  ===============      ===============



See independent accountants' review report and notes to financial statements.
</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.

                                                                                                          SIX MONTHS ENDED
                                                                YEAR ENDED JULY 31,                        JANUARY 31, 1995
                                                  ----------------------------------------------------
PER SHARE DATA:                                     1990         1991       1992        1993        1994      (UNAUDITED)
                                                   ------       ------     ------      ------       ------      ------
<S>                                                <C>          <C>        <C>         <C>          <C>         <C>
    Net asset value, beginning of period           $.9992       $.9996     $1.0000     $1.0000      $1.0000     $.9998
                                                   ------       ------     ------      ------       ------      ------
    INVESTMENT OPERATIONS:
    Investment income_net...............            .0578        .0517       .0359        .0243       .0225      .0149
    Net realized gain (loss) on investments         .0004        .0004       --            --        (.0002)     --
                                                   ------       ------     ------      ------       ------      ------
      TOTAL FROM INVESTMENT OPERATIONS..            .0582        .0521       .0359       .0243        .0223      .0149
                                                   ------       ------     ------      ------       ------      ------
    DISTRIBUTIONS:
    Dividends from investment income_net           (.0578)      (.0517)     (.0359)     (.0243)       (.0225)   (.0149)
    Dividends from net realized gain on
      investments.......................              --            --         --           --            --       --
                                                   ------       ------     ------      ------       ------      ------
      TOTAL DISTRIBUTIONS...............           (.0578)      (.0517)     (.0359)     (.0243)      (.0225)    (.0149)
                                                   ------       ------     ------      ------       ------      ------
    Net asset value, end of period......          $  .9996     $1.0000      $1.0000    $1.0000      $  .9998  $  .9998
                                                   ------       ------     ------      ------       ------      ------
TOTAL INVESTMENT RETURN                             5.93%       5.29%       3.65%       2.46%         2.27%     2.98%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets           .07%       .02%        .20%        .33%          .33%      .46%*
    Ratio of net investment income to average
      net assets........................             5.78%      5.08%       3.59%        2.43%        2.24%     2.94%*
    Decrease reflected in above expense ratios
      due to undertakings by the Manager             .65%        .59%        .41%         .30%         .28%      .15%*
    Net Assets, end of period (000's Omitted)      $281,909    $538,978      $549,383  $608,534    $699,105     $509,266
* Annualized.




See independent accountants' review report and notes to financial statements.
</TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a non-diversified open-end management investment company. Dreyfus Service
Corporation, until August 24, 1994, acted as the distributor of the Fund's
shares, which are sold to the public without a sales load. Dreyfus Service
Corporation is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager"). Effective August 24, 1994, the Manager became a direct
subsidiary of Mellon Bank, N.A.
    On August 24, 1994, Premier Mutual Fund Services, Inc. (the
"Distributor") was engaged as the Fund's distributor. The Distributor,
located at One Exchange Place, Boston, Massachusetts 02109, is a wholly-owned
subsidiary of Institutional Administration Services, Inc., a provider of
mutual fund administration services, the parent company of which is Boston
Institutional Group, Inc.
    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 of $1.00.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Trustees to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Interest income, adjusted
for amortization of premiums and original issue discounts on investments, is
earned from settlement date and recognized on the accrual basis. Realized
gain and loss from securities transactions are recorded on the identified
cost basis.
    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 gain, if any, are normally 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. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (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 Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $8,200
available for Federal income tax purposes to be applied against future net
securities profits, if any realized subsequent to July 31, 1994. The
carryover does not include net realized securities losses from November 1,
1993 through July 31, 1994 which are treated for Federal income tax purposes,
as arising in fiscal 1995. If not applied, the carryover expires in fiscal
2002.
    At January 31, 1995, 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).

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
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 1% of the average
daily value of the Fund's net assets and is payable monthly. The Agreement
provides for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed 1 1/2% of the average value of the Fund's net
assets for any full fiscal year. However, during the six months ended January
31, 1995, the Manager had undertaken to reduce the management fee paid by the
Fund, to the extent that the Fund's aggregate expenses exceeded specified
annual percentages of the Fund's average daily net assets. The reduction in
management fee, pursuant to the undertakings, amounted to $467,104 for the
six months ended January 31, 1995.
    The Manager may modify the expense limitation percentages from time to
time, provided that the resulting expense reimbursement would not be less
than the amount required pursuant to the Agreement.
    (B) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
Dreyfus Service Corporation an amount not to exceed an annual rate of .25 of
1% of the value of the Fund's average daily net assets for servicing
shareholder accounts. The services provided may include personal services
relating to shareholder accounts, such as answering shareholder inquiries
regarding the Fund and providing reports and other information, and services
related to the maintenance of shareholder accounts. During the six months
ended January 31, 1995, the Fund was charged an aggregate of $126,825
pursuant to the Shareholder Services Plan.
    (C) Prior to August 24, 1994, certain officers and trustees of the Fund
were "affiliated persons," as defined in the Act, of the Manager and/or
Dreyfus Service Corporation. Each trustee who is not an "affiliated person"
receives an annual fee of $2,500 and an attendance fee of $250 per meeting.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
    We have reviewed the accompanying statement of assets and liabilities of
General California Municipal Money Market Fund, including the statement of
investments, as of January 31, 1995, and the related statements of operations
and changes in net assets and financial highlights for the six month period
ended January 31, 1995. These financial statements and financial highlights
are the responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
July 31, 1994 and financial highlights for each of the five years in the
period ended July 31, 1994 and in our report dated September 6, 1994, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.



(logo signature)
New York, New York
March 9, 1995


GENERAL CALIFORNIA MUNICIPAL
MONEY MARKET FUND
200 Park Avenue
New York, NY 10166
MANAGER
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166
CUSTODIAN
The Bank of New York
90 Washington Street
New York, NY 10286
TRANSFER AGENT &
DIVIDEND DISBURSING AGENT
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940




Further information is contained
in the Prospectus, which must
precede or accompany this report.




Printed in U.S.A.                            573SA951

General California
Municipal
Money Market Fund
Semi-Annual
Report
January 31, 1995












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