GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1996-09-26
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GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the General California
Municipal Money Market Fund. For its annual reporting period ended July 31,
1996, your Fund produced an annualized yield of 2.89% per share for Class A
shares and 2.53% for Class B shares. Income dividends of approximately $.029
per share were paid during the period for Class A shares and $.025 per share
for Class B shares. Reinvesting these dividends and calculating the effect of
compounding results in annualized effective yields of 2.93% and 2.56% for
Class A shares and Class B shares respectively.* These dividends were exempt
from Federal and State of California personal income taxes, although some
income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.
THE ECONOMY
    The economic expansion which has now lasted more than six years continued
at a healthy clip in recent months with consumer spending, housing activity,
and job growth all showing solid gains. In the second quarter of 1996, the
U.S. economy grew at a 4.2% annual pace, its best performance in two years.
American consumers continued to buy new autos and houses at a robust rate,
with housing sales and starts growing 15.2% in the spring quarter, according
to the government's Gross Domestic Product (GDP) report. At the same time,
the unemployment rate dropped to 5.3% in June, its lowest level in years.
    Vigorous economic growth inevitably brings investor concerns about
inflation: in other words, will the rising economy cause inflation to rise as
well? For much of July, the answer remained clouded. Federal Reserve Board
Chairman Alan Greenspan did not respond to inflationary fears with a clear
indication as to the direction of Fed policy in his July 18 testimony before
Congress. While hinting that the Fed would tighten short-term interest rates
in August if inflationary pressures warranted such action, Mr. Greenspan also
said that he expected the economy to slow of its own accord later this year.
By the end of July, a clearer picture emerged. According to government data
released at month's end, inflation in the second quarter of 1996 climbed just
2.1%, a very modest rise. Both short- and long-term rates responded with
enthusiasm.
MARKET ENVIRONMENT/PORTFOLIO
    If one were to trace the trend in short-term municipal rates over this
most recent semi-annual period, the direction would mirror closely the
changes in supply and demand conditions. The six-month cycle would reflect:
low short-term yields in February due to strong money market fund cash flows
after the New Year; price weakness and higher rates in April as investors
tapped their money market funds to pay income taxes; market strength in late
June to early July as $9 billion in maturing notes left the market; and price
weakness and buying opportunities in late July due to inflationary concerns
and the added supply of summer financings. These technical influences
continue to be the overriding factor affecting municipal money rates.
    These conditions, coupled with action taken by the Federal Reserve Board,
provide the framework for our investment strategy-both on a day-to-day basis
and looking ahead over a one-year horizon. During the first few months of
1996, as a result of uncertainty surrounding potential tax reform, variable
rate demand notes (which currently represent a significant portion of your
Fund's investment portfolio) benefited from unusually high yields. While the
concerns were only temporary, they translated, for a time, into a more
attractive after-tax rate of return than was available to the California tax-
exempt money market investor on taxable instruments with similar maturities.
During this period, the purchase of attractively yielding commercial paper in
the 60- to 90-day range also allowed us to capture returns similar to those on
one-year issues without a significant extension of average maturity-enabling us
to wait out a lower yield environment in anticipation of eventual higher rates.
    The opportunity to commit to longer California-exempt note issues has
appeared in recent weeks and should continue to be available during the
remaining summer months as issuers return to the market with midyear
financings. We have participated in various California note offerings which
resulted in an extension of your Fund's average maturity to the 60-day range.
We will look to take advantage of any additional buying opportunities as we
monitor potential Fed activity and any other significant changes in the
municipal money market. All new investments will continue to meet the high
credit quality standards which we require and to provide a significant level
of liquidity, commensurate with the needs of your Fund.
    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we greatly appreciate your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Sincerely,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
August 15, 1996
New York, N.Y.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.

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<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                              JULY 31, 1996
                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                         AMOUNT           VALUE
                                                                                                       _______        _______
<S>                                                                                             <C>             <C>
CALIFORNIA-88.0%
Alameda County, TRAN 4.50%, 6/30/97.........................................                    $    6,500,000  $   6,531,364
Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)
    3.55% (LOC; National Bank of Canada) (a,b)..............................                         8,850,000      8,850,000
California Housing Finance Agency:
    Home Mortgage Revenue:
      3.55%, Series D, 4/1/97 (GIC; FGIC)...................................                        11,500,000     11,500,000
      4%, Series J, 7/24/97 (GIC; FGIC).....................................                         7,000,000      7,000,000
    Multi-Family Revenue, Refunding, VRDN
      3.25%, Series B (Corp. Guaranty; FNMA) (a)............................                         5,600,000      5,600,000
California Pollution Control Financing Authority:
    PCR:
      (Pacific Gas and Electric):
          CP 3.40%, 9/24/96 (LOC; Morgan Guaranty Trust Co.) (b)............                        10,000,000     10,000,000
          Refunding, VRDN 3.60%, Series B (LOC; Rabobank Nederland) (a,b)...                         5,000,000      5,000,000
      (San Diego Gas and Electric)
          4%, Series A, 9/1/96 (Corp. Guaranty; San Diego Gas and Electric).                         7,500,000      7,500,000
    VRDN:
      RRR:
          (Delano Project) 3.65% (LOC; ABN-Amro Bank) (a,b).................                         8,900,000      8,900,000
          Refunding:
            (Ultra Power Malaga Project) 3.70%, Series B (LOC; Bank of America) (a,b)                5,500,000      5,500,000
            (Ultra Power Rocklin Project) 3.70%, Series B (LOC; Bank of America) (a,b)               3,500,000      3,500,000
      SWDR (Colmac Energy Project) 3.55%, Series A (LOC; Swiss Bank Corp.) (a,b)                     6,500,000      6,500,000
California School Cash Reserve Program Authority, Notes
    4.75%, Series A, 7/2/97 (Insured; MBIA).................................                        14,000,000     14,100,683
California Statewide Community Development Authority, VRDN:
    Apartment Development Revenue, Refunding:
      3.20%, Series A-6 (Corp. Guaranty; FNMA) (a)..........................                         6,400,000      6,400,000
      3.30%, Series A-7 (Corp. Guaranty; FNMA) (a)..........................                         6,500,000      6,500,000
    COP, Revenue:
      Refunding (Kaiser Foundation Hospital)
          3.25% (Corp. Guaranty; Kaiser Permanente) (a).....................                         5,000,000      5,000,000
      (Sutter Health Obligation Group)
          3.40% (Insured; AMBAC and Liquidity Facility; Industrial Bank of  Japan) (a)               6,200,000      6,200,000
    Multi-Family Revenue (Canyon Creek Apartments)
      3.50%, Series C (Corp. Guaranty; FNMA) (a)............................                        11,800,000     11,800,000
City of Camarillo, MFHR, VRDN (Heritage Park)
    3.35%, Series A (Corp. Guaranty; FNMA) (a)..............................                         6,700,000      6,700,000
Fresno, MFHR, Refunding, VRDN (Heron Pointe Apartments)
    3.45% (LOC; First Interstate Bank of California) (a,b)..................                         5,400,000      5,400,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                       JULY 31, 1996
                                                                                                      PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT           VALUE
                                                                                                       _______        _______
CALIFORNIA (CONTINUED)
Golden Empire Schools Financing Authority, VRDN (Kern High School District)
    3.25% (LOC: Canadian Imperial Bank of Commerce and
    National Westminster Bank) (a,b)........................................                    $    7,400,000  $   7,400,000
City of Hayward Housing Authority, Multi-Family Revenue, Refunding, VRDN
    (Barrington Hills) 3.40%, Series A (Corp. Guaranty; FNMA) (a)...........                        13,550,000     13,550,000
Huntington Beach, MFHR, VRDN:
    (Five Points Seniors Project) 3.50%, Series A (LOC; Wells Fargo Bank) (a,b)                      3,100,000      3,100,000
    (Mercury Savings and Loan Village)
      4.55%, Series A (LOC; Resolution Funding Corp.) (a,b).................                         6,000,000      6,000,000
Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.775% (LOC; Bankers Trust) (a,b)                    3,000,000      3,000,000
City of Los Angeles, TRAN 4.50%, 6/19/97....................................                         6,000,000      6,026,488
Los Angeles, MFHR, VRDN:
    (Beverly Park Apartments) 3.40%, Series A (LOC; Barclays Bank) (a,b)....                         9,600,000      9,600,000
    (Loans To Lender Program):
      3.65%, Series A (LOC; Federal Home Loan Banks) (a,b)..................                         4,300,000      4,300,000
      3.65%, Series B (LOC; Federal Home Loan Banks) (a,b)..................                         7,500,000      7,500,000
    (Lucas Studios Project) 3.65%, Series D (LOC; Bank of America) (a,b)....                         3,655,000      3,655,000
    (Oakwood Apartments) 3.85%, Series B (LOC; Sumitomo Bank) (a,b).........                         9,605,000      9,605,000
Los Angeles County:
    Pension Obligation, Refunding, VRDN
      3.40%, Series C (Insured; AMBAC and SBPA; Bank of Nova Scotia) (a)....                         5,000,000      5,000,000
    TRAN 4.50%, 6/30/97 (LOC: Bank of America, Credit Suisse,
      Morgan Guaranty Trust Co., Union Bank of Switzerland and
      West Deutsche Landesbank) (b).........................................                        14,500,000     14,579,160
Los Angeles County Metropolitan Transportation Authority, Revenue:
    CP 3.50%, 10/8/96 (LOC: ABN-Amro, Bank of California, Banque Nationale de
Paris,
      Canadian Imperial Bank of Commerce and National Westminster Bank) (b).                         3,900,000      3,900,000
    VRDN (General Union Station Gateway)
      2.25%, Series A (BPA; Societe Generale and Insured; FSA) (a)..........                        11,000,000     11,000,000
Olcese Water District, COP, CP (Rio Bravo Water Delivery System Program)
    3.80%, Series A, 8/8/96 (LOC; Sumitomo Bank) (b)........................                         8,800,000      8,800,000
City of Redland Sewer Facility Refunding, COP, VRDN
    3.50% (Insured; FGIC and Liquidity Facility; FGIC) (a)..................                         8,000,000      8,000,000
Sacramento County Housing Authority, MFHR, VRDN (Stone Creek Apartments
Project)
    3.55%, Series L (LOC; First Interstate Bank of California) (a,b)........                         5,450,000      5,450,000
Sacramento Municipal Utility District, Electric Revenue, CP:
    3.50%, Series 1, 10/17/96 (LOC; Bayerische Landesbank) (b)..............                         6,993,000      6,993,000
    3.55%, Series 1, 10/17/96 (LOC; Bayerische Landesbank) (b)..............                         8,467,000      8,467,000
San Bernardino County, COP, VRDN 3.73% (LOC; Sumitomo Bank) (a,b)...........                        12,000,000     12,000,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                     JULY 31, 1996
                                                                                                      PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT           VALUE
                                                                                                       _______        _______
CALIFORNIA (CONTINUED)
San Diego County, TRAN
    4.50%, 9/30/96 (LOC: Banque Nationale de Paris and National Westminster) (b)                 $  12,000,000  $  12,021,744
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
    (French Co. Project) 3.65% (LOC; Credit Commercial de France) (a,b).....                         3,800,000      3,800,000
San Francisco City and County Redevelopment Agency, Multi-Family Revenue,
VRDN
    (Bayside Village Project) 3.60%, Series B (LOC; Industrial Bank of Japan) (a,b)                  4,500,000      4,500,000
San Jose Redevelopment Agency, Revenue, VRDN (Merged Area Redevelopment
Project)
    3.35%, Series B (LOC; Morgan Guaranty Trust Co.) (a,b)..................                         5,000,000      5,000,000
South Coast Education Agencies, Partnerships Pooled 5%, 8/14/96.............                        11,000,000     11,001,869
Vacaville, MFMR, VRDN (Quail Run) 3.25%, Series A (Corp. Guaranty; FNMA) (a)                         2,900,000      2,900,000
U.S. RELATED-12.0%
Commonwealth of Puerto Rico Government Development Bank, CP:
    3.15%, 8/27/96..........................................................                        10,000,000     10,000,000
    3.40%, 8/12/96..........................................................                         5,000,000      5,000,000
    3.55%, 10/8/96..........................................................                         3,000,000      3,000,000
    3.50%, 10/10/96.........................................................                        10,000,000     10,000,000
    3.55%, 10/10/96.........................................................                        19,000,000     19,000,000
                                                                                                                      ______
TOTAL INVESTMENTS (cost $392,631,308).......................................                                     $392,631,308
                                                                                                                      =======
</TABLE>

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<CAPTION>



GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND

SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>     <C>
AMBAC         American Municipal Bond Assurance Corporation      MBIA    Municipal Bond Investors Assurance
BPA           Bond Purchase Agreement                                         Insurance Corporation
COP           Certificate of Participation                       MFHR    Multi-Family Housing Revenue
CP            Commercial Paper                                   MFMR    Multi-Family Mortgage Revenue
FGIC          Financial Guaranty Insurance Company               PCR     Pollution Control Revenue
FNMA          Federal National Mortgage Association              RRR     Resources Recovery Revenue
FSA           Financial Security Assurance                       SBPA    Standby Bond Purchase Agreement
GIC           Guaranteed Investment Contract                     SWDR    Solid Waste Disposal Revenue
IDR           Industrial Development Revenue                     TRAN    Tax and Revenue Anticipation Notes
LOC           Letter of Credit                                   VRDN    Variable Rate Demand Notes
</TABLE>

<TABLE>
<CAPTION>


SUMMARY OF COMBINED RATINGS (UNAUDITED)
MOODY'S                             OR                STANDARD & POOR'S                        PERCENTAGE OF VALUE
- -------                                               -----------------                        ------------------
<S>                                                   <C>                                          <C>
VMIG1/MIG1, P1 (c)                                    SP1+/SP1, A1+/A1 (c)                          91.7%
Aaa/Aa (d)                                            AAA/AA (d)                                     5.9
Not Rated (e)                                         Not Rated (e)                                  2.4
                                                                                                   ____
                                                                                                   100.0%
                                                                                                   ====
</TABLE>

NOTES TO STATEMENT OF INVESTMENTS:
    (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 July 31, 1996, 48.9% of the Fund's
    net assets are backed by letters of credit issued by  domestic banks,
    foreign banks and government agencies.
    (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 July 31, 1996, the Fund had $139,910,000 (35.4% of net assets)
    invested in securities whose payment of prinicipal and interest is
    dependent upon revenues generated from housing projects.






See notes to financial statements.
<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                                       JULY 31, 1996
<S>
ASSETS:                                                                                         <C>               <C>
    Investments in securities, at value-Note 1(a)...........................                                      $392,631,308
    Cash....................................................................                                         1,515,177
    Interest receivable.....................................................                                         1,785,389
    Prepaid expenses........................................................                                            34,504
                                                                                                                       ______
                                                                                                                   395,966,378
LIABILITIES:
    Due to The Dreyfus Corporation and affiliates...........................                    $210,125
    Due to Distributor......................................................                         706
    Accrued expenses and other liabilities..................................                     125,847               336,678
                                                                                                   ____                ______
NET ASSETS  ................................................................                                      $395,629,700
                                                                                                                       =======
REPRESENTED BY:
    Paid-in capital.........................................................                                      $395,803,373
    Accumulated net realized (loss) on investments..........................                                          (173,673)
                                                                                                                       ______
NET ASSETS at value.........................................................                                      $395,629,700
                                                                                                                       =======
Shares of Beneficial Interest outstanding:
    Class A Shares
      (unlimited number of $.001 par value shares authorized)...............                                       390,328,603
                                                                                                                       =======
    Class B Shares
      (unlimited number of $.001 par value shares authorized)...............                                         5,474,770
                                                                                                                       =======
NET ASSET VALUE per share:
    Class A Shares
      ($390,154,930 / 390,328,603 shares)...................................                                             $1.00
                                                                                                                       =======
    Class B Shares
      ($5,474,770 / 5,474,770 shares).......................................                                             $1.00
                                                                                                                       =======


See notes to financial statements.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS                                                                        YEAR ENDED JULY 31, 1996
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                       $15,651,463
    EXPENSES:
      Management fee-Note 2(a)..............................................                     $2,195,288
      Shareholder servicing costs-Note 2(c).................................                        483,684
      Professional fees.....................................................                         62,389
      Custodian fees........................................................                         47,135
      Trustees' fees and expenses-Note 2(d).................................                         24,183
      Registration fees.....................................................                         18,578
      Prospectus and shareholders' reports..................................                         13,492
      Distribution fees (Class B)-Note 2(b).................................                            341
      Miscellaneous.........................................................                         17,673
                                                                                                      _____
          TOTAL EXPENSES....................................................                      2,862,763
      Less-reduction in shareholder servicing cost due to undertaking-Note 2(c)                         144
                                                                                                      _____
          NET EXPENSES......................................................                                         2,862,619
                                                                                                                        ______
INVESTMENT INCOME-NET.......................................................                                        12,788,844
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                           (25,274)
                                                                                                                        ______
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                       $12,763,570
                                                                                                                        ======




See notes to financial statements.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                              YEAR ENDED JULY 31,
                                                                                         ------------------------------
                                                                                             1995             1996
                                                                                          ---------          ---------
OPERATIONS:
    Investment income-net.............................................            $      16,752,063     $  12,788,844
    Net realized (loss) on investments................................                      (28,743)          (25,274)
                                                                                          ________          ________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                   16,723,320        12,763,570
                                                                                          ________          ________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................                  (16,752,063)      (12,784,667)
      Class B shares..................................................                          --             (4,177)
                                                                                          ________          ________
          TOTAL DIVIDENDS.............................................                  (16,752,063)      (12,788,844)
                                                                                          ________          ________
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................                1,802,148,457     1,393,367,866
      Class B shares..................................................                          --          5,485,204
    Dividends reinvested:
      Class A shares..................................................                   15,289,984        11,495,460
      Class B shares..................................................                          --              4,177
    Cost of shares redeemed:
      Class A shares..................................................               (2,053,110,924)   (1,478,086,875)
      Class B shares..................................................                          --            (14,611)
                                                                                          ________          ________
          (DECREASE) IN NET ASSETS FROM BENEFICIAL INTEREST TRANSACTIONS               (235,672,483)      (67,748,779)
                                                                                          ________          ________
            TOTAL (DECREASE) IN NET ASSETS............................                 (235,701,226)      (67,774,053)
NET ASSETS:
    Beginning of year.................................................                  699,104,979       463,403,753
                                                                                          ________          ________
    End of year.......................................................             $    463,403,753  $    395,629,700
                                                                                          =========         =========

</TABLE>


See notes to financial statements.
<TABLE>
<CAPTION>


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 year indicated. This
information has been derived from the Fund's financial statements.

                                                                         CLASS A SHARES                      CLASS B SHARES
                                                     __________________________________________________         _______
                                                                                                               YEAR ENDED
                                                                        YEAR ENDED JULY 31,                     JULY 31,
                                                     __________________________________________________
PER SHARE DATA:                                      1992        1993        1994        1995        1996          1996*
                                                     ----        ----        ----        ----        ----          ----
    <S>                                           <C>         <C>         <C>         <C>         <C>           <C>
    Net asset value, beginning of year....        $  1.00     $  1.00     $  1.00     $  1.00     $  1.00       $  1.00
                                                     ----        ----        ----        ----        ----          ----
    INVESTMENT OPERATIONS;
    Investment income-net.................           .036        .024        .023        .031        .029          .025
                                                     ----        ----        ----        ----        ----          ----
    DISTRIBUTIONS;
    Dividends from investment income-net..          (.036)      (.024)      (.023)      (.031)      (.029)        (.025)
                                                     ----        ----        ----        ----        ----          ----
    Net asset value, end of year..........        $  1.00     $  1.00     $  1.00     $  1.00     $  1.00       $  1.00
                                                     ====        ====        ====        ====        ====          ====
TOTAL INVESTMENT RETURN...................           3.65%       2.46%       2.27%       3.14%       2.94%         2.56%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets           .20%        .33%        .33%        .52%        .65%         1.00%
    Ratio of net investment income
      to average net assets...............           3.59%       2.43%       2.24%       3.07%       2.91%         2.45%
    Decrease reflected in above expense ratios
      due to undertakings by the Manager..            .41%        .30%        .28%        .11%         -           .08%
    Net Asset, end of year (000's Omitted)       $549,383    $608,534    $699,105    $463,404    $390,155        $5,475
    *From August 1, 1995 (commencement of initial offering) to July 31, 1996.

</TABLE>


See notes to financial statements.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    General California Municipal Money Market Fund (the "Fund") is registered
under the Investment Company Act of 1940 ("Act") as a non-diversified
open-end management investment company. The Fund's investment objective is to
maximize current income exempt from Federal and State of California income
taxes to the extent consistent with the preservation of capital and the
maintenance of liquidity. The Dreyfus Corporation ("Manager") serves as the
Fund's investment adviser. The Manager is a direct subsidiary of Mellon Bank,
N.A. Premier Mutual Fund Services, Inc. (the "Distributor") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales charge.
    On July 19, 1995, the Fund's Board of Trustees approved an amendment to
the Fund's Agreement and Declaration of Trust to provide for the issuance of
additional shares of the Fund. The amendment was approved by Fund
shareholders on September 1, 1994. Pursuant to the amendment, the Fund's
existing authorized shares were classified as Class A shares and an unlimited
number of authorized and unissued shares of Beneficial Interest of the Fund,
par value $.001 per share, were classified as Class B shares. The Fund began
offering both Class A and Class B shares on August 1, 1995. Class A shares
and Class B shares are identical except as to the services offered to and the
expenses borne by each class and certain voting rights. Class B shares are
subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act
and, in addition, Class B shares are charged directly for sub-accounting
services provided by service agents at an annual rate of .05% of the value of
the average daily net assets of Class B.
    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.
    The Fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management
estimates and assumptions. Actual results could differ from those estimates.
    (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. 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 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.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    (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 $155,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to July 31, 1996. The
carryover does not include net realized securities losses from November 1,
1995 through July 31, 1996 which are treated for Federal income tax purposes,
as arising in fiscal 1997. If not applied, $8,200 of the carryover expires in
fiscal 2002, $113,800 expires in fiscal 2003 and $33,000 expires in fiscal
2004.
    At July 31, 1996, 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 1% of the value
of the Fund's average daily 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. There was no expense reimbursement for the
year ended July 31, 1996.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, effective
August 1, 1995, the Fund directly bears the cost of preparing, printing and
distributing prospectuses and statements of additional information and of
implementing and operating the Class B Distribution Plan. In addition, the
Fund reimburses the Distributor for payments made to third parties for
distributing Class B shares at an aggregate annual rate up to .20 of 1% of
the value of the average daily net assets of Class B. During the year ended
July 31, 1996, $341 was charged to the Fund pursuant to the Class B
Distribution Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, with respect to
Class A ("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus
Service Corporation, a wholly-owned subsidiary of the Manager, an amount not
to exceed an annual rate of .25 of 1% of the value of the Fund's average
daily net of assets of Class A 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 regarding the Fund and providing reports
and other information, and services related to the maintenance of shareholder
accounts. During the year ended July 31, 1996, the Fund was charged an
aggregate of $296,095 pursuant to the Class A Shareholder Services Plan.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), effective August 1, 1995, the Fund pays the
Distributor, at an annual rate of .25 of 1% 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 the Fund and providing reports and
other information, and services related to the maintenance of shareholder
accounts. The Distributor may make payments to Service Agents (a securities
dealer, financial institution or other industry professional) in respect of
their services. The Distributor determines the amounts to be paid to Service
Agents.
    The Manager has currently undertaken through July 31, 1997, that if the
aggregate expenses of Class B of the Fund (exclusive of certain expenses as
described above) exceed 1% of the value of the average daily net assets of
Class B, the Manager will reimburse the expenses of the Fund under the
Shareholder Services Plan relating to Class B to the extent of any excess
expense and up to the full fee payable under such Plan. During the year ended
July 31, 1996, $512 was charged to the Fund pursuant to the Class B
Shareholder Services Plan, of which $144 was reimbursed by the Manager.
    Effective December 1, 1995, the Fund compensates Dreyfus Transfer, Inc.,
a wholly-owned subsidiary of the Manager, under a transfer agency agreement
for providing personnel and facilities to perform transfer agency services
for the Fund. Such compensation amounted to $74,947 during the year ended
July 31, 1996.
    (D) Each trustee who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $250
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
    We have audited the accompanying statement of assets and liabilities of
General California Municipal Money Market Fund, including the statement of
investments, as of July 31, 1996, and the related statement of operations for
the year then ended, the statement of changes in net assets for each of the
two years in the period then ended and financial highlights for each of the
years indicated therein. These financial statements and financial highlights
are the responsibility of the Fund's management. Our responsibility is to
express an opinion on these financial statements and financial highlights
based on our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements. Our procedures included confirmation of
securities owned as of July 31, 1996 by correspondence with the custodian. An
audit also includes assessing the accounting principles used and significant
estimates made by management, as well as evaluating the overall financial
statement presentation. We believe that our audits provide a reasonable basis
for our opinion.
    In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the financial
position of General California Municipal Money Market Fund at July 31, 1996,
the results of its operations for the year then ended, the changes in its net
assets for each of the two years in the period then ended, and the financial
highlights for each of the indicated years, in conformity with generally
accepted accounting principles.

                              [Ernst and Young LLP signature logo]
New York, New York
September 4, 1996


GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
IMPORTANT TAX INFORMATION (UNAUDITED)
    In accordance with Federal tax law, the Fund hereby designates all the
dividends paid from investment income-net during the fiscal year ended July
31, 1996 as "exempt-interest dividends" (not subject to regular Federal and,
for individuals who are California residents, California personal income
taxes).


[Dreyfus lion "d" logo]
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
Dreyfus Transfer, Inc.
P.O. Box 9671
Providence, RI 02940











Printed in U.S.A.                        573/699AR967
[Dreyfus logo]
General California
Municipal
Money Market Fund
Annual Report
July 31, 1996



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