GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1997-09-30
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GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to report the performance for General California Municipal
Money Market Fund for its fiscal year ended July 31, 1997 as shown in the
following table:
<TABLE>
                                                                                                   ANNUALIZED
                                                                        YIELD                   EFFECTIVE YIELD*
                                                                   --------------                --------------
<S>                                                                     <C>                          <C>
           Class A Shares.........................                      2.91%                        2.95%
           Class B Shares.........................                      2.58%                        2.61%
</TABLE>
THE ECONOMY
    The latest government data continued to show the U.S. economy growing at
a somewhat decelerated pace, with real Gross Domestic Product (GDP) falling
to approximately 2.2% during the April-to-June quarter. In June, stronger
chain store activity was balanced by tumbling vehicle sales, while the big
three car makers sweetened sales incentive plans, signaling a belief that
demand will remain on the soft side through the summer. In fact, consumer
spending has been weak since the spring, expanding at just 0.8% in the second
quarter. Nonetheless, many economists expect growth to pick up again,
pointing to brisk capital outlays by businesses and a combination of low
interest rates, high consumer confidence, steady job gains, huge wealth
creation, and rising disposable income that should soon jump-start consumer
spending.
    Meanwhile, the economy's strength continues to be complemented by a
virtual lack of inflation. With consumer prices rising just 1.4% during the
second quarter, inflation is running at its lowest pace in 34 years.
Moreover, U.S. producer prices fell a record seventh consecutive month in
July, and falling gold and oil prices have supported the view that inflation
is also moderate globally. As expected, the Federal Reserve Board's Open
Market Committee (FOMC) left interest rates alone at its July meeting, while
Fed Chairman Alan Greenspan all but ruled out a move to tighten monetary
policy anytime soon at his semi-annual testimony before the Senate on July
23. In the money market, short-term rates remained within a trading range as
market participants deemed a Fed move in August unlikely.
MARKET ENVIRONMENT/PORTFOLIO OVERVIEW
    Each year, as summer approaches, the short-term municipal market
experiences volatility that is reflective of the changing patterns of supply
and demand conditions during the period. These market "technicals" require
adjustments to portfolio strategy in anticipation of conditions such as: an
increase in supply due to funds experiencing redemptions (April tax season);
a dearth of supply of high quality issues (end of June); and substantial new
money market issuance (mid-July financings). Our portfolio adjustments
attempt to structure your Fund to take advantage of these conditions in an
effort to enhance your Fund's return, while maintaining our commitment to
high quality holdings.
    In response to the expected changes in both cash flow and supply
conditions, we began preparations in early June for extending your Fund's
average maturity. By creating a calendar of upcoming California issues and by
subjecting each new issue to rigorous in-house credit review, we were
positioned to purchase those notes which we believed would be attractive
holdings for your Fund. As various new issues came to the short-term market
during early summer, we selectively purchased notes which would add value to
your Fund. At all times, we will continue to commit to only those California
issues which meet our high quality investment guidelines and which provide
the appropriate level of liquidity for your Fund's needs. Additionally, we
will monitor all conditions which affect our marketplace and adjust our
investment policy where necessary to pursue competitive returns.

    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 appreciate greatly your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Very truly yours,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
August 18, 1997
New York, N.Y.

*Effective yield takes into account the effect of compounding and is based
upon dividends declared daily and reinvested monthly.

<TABLE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                                             JULY 31, 1997
                                                                                                     Principal
Tax Exempt Investments-100.0%                                                                          Amount          Value
                                                                                                       -------        -------
<S>                                                                                            <C>              <C>
California-98.5%
Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)
  3.60% (LOC; National Bank of Canada) (a,b)................................                    $    8,850,000  $   8,850,000
State of California, CP
  3.60%, 8/5/97 (Liquidity Facility: Bayerische Landesbank, Credit Suisse,
  Landesbank Hessen, Morgan Guaranty Trust Co. and Westdeutsche Landesbank).                         7,000,000      7,000,000
California Health Facilities Finance Authority, Revenue, VRDN:
  (Catholic Health Care)
    3.35%, Series D (Insured; MBIA and Liquidity Facility; Rabobank Nederland) (a)                  10,400,000     10,400,000
  Refunding (Catholic West)
    3.35%, Series D (Insured; MBIA and Liquidity Facility; Rabobank Nederland) (a)                   9,500,000      9,500,000
California Housing Finance Agency:
  Home Mortgage Revenue
    3.95%, Series J, 8/3/98 (Insured; FGIC).................................                        14,000,000     14,000,000
  Multi-Family Revenue, Refunding, VRDN
    3.35%, Series B (Corp. Guaranty; FNMA) (a)..............................                         5,600,000      5,600,000
  Single Family Mortgage Purchase
    3.70%, Series B, 4/1/98 (LOC; Morgan Stanley and Co.) (b)...............                         9,000,000      9,000,000
California Pollution Control Financing Authority:
  PCR:
    Refunding (Pacific Gas and Electric):
    CP 3.85%, Series E, 9/12/97 (LOC; Morgan Guaranty Trust Co.) (b)........                        10,000,000     10,000,000
    VRDN:
      3.35%, Series C (LOC; Bank of America) (a,b)..........................                         4,400,000      4,400,000
      3.45%, Series B (LOC; Rabobank Nederland) (a,b).......................                         5,000,000      5,000,000
  VRDN:
    RRR, Refunding (Ultra Power Malaga Project):
      3.50%, Series A (LOC; Bank of America) (a,b)..........................                         1,000,000      1,000,000
      3.50%, Series B (LOC; Bank of America) (a,b)..........................                         3,100,000      3,100,000
    SWDR (Colmac Energy Project) 3.40%, 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, 7/2/98 (Insured; AMBAC)..................................                        14,000,000     14,111,275
California Statewide Community Development Authority:
  Revenue 4.50%, Series A, 6/30/98 (Insured; FSA and LOC; California Statewide) (b)                 10,000,000     10,061,477
  VRDN:
    Apartment Development Revenue, Refunding
      3.45%, Series A-7 (Corp. Guaranty; FNMA) (a)..........................                         6,500,000      6,500,000
    COP (North California Retirement Officers)
      3.40% (LOC; Dresdner Bank) (a,b)......................................                         3,600,000      3,600,000
    Multi-Family Revenue (Canyon Creek Apartments)
      3.55%, Series C (Corp. Guaranty; FNMA) (a)............................                        11,800,000     11,800,000
City of Camarillo, MFHR, VRDN (Heritage Park)
  3.45%, Series A (Corp. Guaranty; FNMA) (a)................................                         6,800,000      6,800,000
Chula Vista, IDR, Refunding, VRDN (San Diego Gas)
  3.45%, Series A (Corp. Guaranty; San Diego Gas and Electric) (a)..........                         5,000,000      5,000,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                           JULY 31, 1997
                                                                                                      Principal
Tax Exempt Investments (continued)                                                                     Amount          Value
                                                                                                       -------        -------
California (continued)
City of Clovis, MFHR, VRDN (Fowler Place Apartments Project)
  3.50% (LOC; Wells Fargo Bank) (a,b).......................................                    $    7,400,000  $   7,400,000
Fresno, MFHR, Refunding, VRDN (Heron Pointe Apartments)
  3.45% (LOC; First Interstate Bank of California) (a,b)....................                         5,200,000      5,200,000
Golden Empire Schools Financing Authority, VRDN (Kern High School District)
  3.50% (LOC: Canadian Imperial Bank of Commerce and National Westminster Bank) (a,b)                7,200,000      7,200,000
City of Hayward Housing Authority, Multi-Family Revenue, Refunding, VRDN
  (Barrington Hills) 3.45%, Series A (Corp. Guaranty; FNMA) (a).............                        13,550,000     13,550,000
Huntington Beach, MFHR, VRDN (Five Points Seniors Project)
  3.60%, Series A (LOC; Wells Fargo Bank) (a,b).............................                         3,100,000      3,100,000
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:
  (Beverly Park Apartments) 3.50%, Series A (LOC; Chase Manhattan Bank) (a,b)                        9,600,000      9,600,000
  (Loans To Lender Program):
    3.50%, Series A (LOC; Federal Home Loan Banks) (a,b)....................                         2,300,000      2,300,000
    3.50%, 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) 3.65%, Series B (LOC; Sumitomo Bank) (a,b)...........                         9,555,000      9,555,000
Los Angeles County:
  Pension Obligation, Refunding, VRDN
    3.35%, Series C (Insured; AMBAC and Liquidity Facility; Bank of Nova Scotia) (a)                 8,000,000      8,000,000
  TRAN 4.50%, 6/30/98.......................................................                        10,000,000     10,057,086
Los Angeles County Metropolitan Transportation Authority, Sales Tax Revenue,
Refunding
  VRDN 3.35%, Series A (Insured; MBIA and Liquidity Facility; Credit Locale de France) (a)          16,100,000     16,100,000
Metropolitan Water District, Water Works Revenue, Refunding, VRDN
  3.35%, Series A (Insured; AMBAC and LOC; ABN-Amro Bank) (a,b).............                        10,200,000     10,200,000
Oakland Unified School District, TRAN 4.25%, 10/14/97.......................                         8,000,000      8,005,855
Olcese Water District, COP, CP (Rio Bravo Water Delivery System Program)
  3.85%, Series A, 10/22/97 (LOC; Sumitomo Bank) (b)........................                         8,800,000      8,800,000
Ontario Redevelopment Agency, Revenue, VRDN (Mission Oaks)
  3.75%, Series A (LOC; Union Bank of California) (a,b).....................                         5,770,000      5,770,000
Orange County, COP, VRDN (Sanitation Districts # 1-3, 5-7, 11, 13, 14)
  3.45%, Series A (LOC; National Westminster Bank) (a,b)....................                         9,200,000      9,200,000
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
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
  (French Co. Project) 3.40% (LOC; Credit Commercial De France) (a,b).......                         3,400,000      3,400,000
San Francisco City and County Redevelopment Agency, Multi-Family Revenue,
VRDN
  (Bayside Village Project) 3.725%, Series B (LOC; Industrial Bank of Japan) (a,b)                   4,500,000      4,500,000
San Jose, MFHR, VRDN (Sienna at Renaissance)
  3.60%, Series A (LOC; Bank One of Arizona) (a,b)..........................                         5,000,000      5,000,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                        JULY 31, 1997
                                                                                                     Principal
Tax Exempt Investments (continued)                                                                     Amount          Value
                                                                                                       -------        -------
U.S. Related-1.5%
Commonwealth of Puerto Rico Government Development Bank, CP 3.70%, 8/11/97..                    $    5,000,000  $   5,000,000
                                                                                                                      -------
TOTAL INVESTMENTS (cost $323,765,693).......................................                                     $323,765,693
                                                                                                                      =======
Summary of Abbreviations
AMBAC         American Municipal Bond Assurance Corporation      MBIA    Municipal Bond Investors Assurance
COP           Certificate of Participation                                    Insurance Corporation
CP            Commercial Paper                                   MFHR    Multi-Family Housing Revenue
FGIC          Financial Guaranty Insurance Company               PCR     Pollution Control Revenue
FNMA          Federal National Mortgage Association              RRR     Resources Recovery Revenue
FSA           Financial Security Assurance                       SWDR    Solid Waste Disposal Revenue
IDR           Industrial Development Revenue                     TRAN    Tax and Revenue Anticipation Notes
LOC           Letter of Credit                                   VRDN    Variable Rate Demand Notes
Summary of Combined Ratings (Unaudited)
Fitch (c)              or          Moody's             or         Standard & Poor's          Percentage of Value
- -------                            -------                       ------------------          -------------------
F1+/F1                             VMIG1/MIG1, P1 (d)             SP1+/SP1, A1+/A1 (d)              92.7%
AAA/AA (e)                         Aaa/Aa (e)                     AAA/AA (e)                         3.4
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                      3.9
                                                                                                   ----
                                                                                                   100.0%
                                                                                                   ====
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, 1997, 52.5% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, government agencies and brokerage firms.
    (c)  Fitch currently provides creditworthiness information for a limited
    number of investements.
    (d)  P1 and A1 are the highest ratings assigned tax exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (e)  Notes which are not F, MIG or SP rated are represented by bond
    ratings of the issuers.
    (f)  Securities which, while not rated by Fitch, Moody's and Standard &
    Poor's have been determined by the Manager to be of comparable quality to
    those rated securities in which the Fund may invest.
    (g)  At July 31, 1997, the Fund had $145,130,000 (44.2% of net assets)
    invested in securities whose payment of principal and interest is
    dependent upon revenues generated from housing projects.







SEE NOTES TO FINANCIAL STATEMENTS.

</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                                               JULY 31, 1997
                                                                                                       Cost            Value
                                                                                                     -------           -------
<S>                                                                                             <C>               <C>
ASSETS:                          Investments in securities-See Statement of Investments         $323,765,693      $323,765,693
                                 Cash.......................................                                         3,401,517
                                 Interest receivable........................                                         1,299,326
                                                                                                                       -------

                                                                                                                   328,466,536
                                                                                                                       -------
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates                                         244,776
                                 Due to Distributor.........................                                             1,503
                                 Accrued expenses...........................                                            65,739
                                                                                                                       -------

                                                                                                                       312,018
                                                                                                                       -------
NET ASSETS..................................................................                                      $328,154,518
                                                                                                                       =======
REPRESENTED BY:                  Paid-in capital............................                                      $328,348,391
                                 Accumulated net realized gain (loss) on investments                                  (193,873)
                                                                                                                       -------
NET ASSETS..................................................................                                      $328,154,518
                                                                                                                       =======
                                                     NET ASSET VALUE PER SHARE
                                                ----------------------------------
                                                                                                     Class A           Class B
                                                                                                     -------           -------
Net Assets..................................................................                    $327,226,190   $       928,328
Shares Outstanding..........................................................                     327,420,030           928,361
NET ASSET VALUE PER SHARE...................................................                           $1.00             $1.00
                                                                                                         ===               ===










SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS
                                                                              YEAR ENDED JULY 31, 1997
<S>                                                                                               <C>              <C>
INVESTMENT INCOME
INCOME                           Interest Income............................                                       $13,031,545
EXPENSES:                        Management fee-Note 2(a)...................                      $1,836,034
                                 Shareholder servicing costs-Note 2(c)......                         338,290
                                 Professional fees..........................                          57,466
                                 Custodian fees.............................                          38,866
                                 Trustees' fees and expenses-Note 2(d)......                          26,408
                                 Registration fees..........................                          23,702
                                 Prospectus and shareholders' reports.......                           9,865
                                 Distribution fees (Class B)-Note 2(b)......                           7,812
                                 Miscellaneous..............................                          15,690
                                                                                                      ------
                                       Total Expenses.......................                       2,354,133
                                 Less-reduction in shareholder servicing costs due to
                                     undertaking-Note 2(c)..................                          (2,734)
                                                                                                      ------
                                       Net Expenses.........................                                         2,351,399
                                                                                                                       -------
INVESTMENT INCOME-NET.......................................................                                        10,680,146
NET REALIZED GAIN (LOSS) ON INVESTMENTS-Note 1(b)...........................                                           (20,200)
                                                                                                                       -------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                       $10,659,946
                                                                                                                       =======













SEE NOTES TO FINANCIAL STATEMENTS.

</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                         Year Ended       Year Ended
                                                                                       July 31, 1997    July 31, 1996
                                                                                         ---------         ---------
<S>                                                                            <C>                      <C>
OPERATIONS:
  Investment income-net..................................................       $       10,680,146      $ 12,788,844
  Net realized gain (loss) on investments................................                  (20,200)          (25,274)
                                                                                         ---------         ---------
      Net Increase (Decrease) in Net Assets Resulting from Operations....               10,659,946        12,763,570
                                                                                         ---------         ---------
DIVIDENDS TO SHAREHOLDERS FROM:
  Investment income-net:
    Class A shares.......................................................              (10,581,881)      (12,784,667)
    Class B shares.......................................................                  (98,265)           (4,177)
                                                                                         ---------         ---------
      Total Dividends....................................................              (10,680,146)      (12,788,844)
                                                                                         ---------         ---------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold:
    Class A shares.......................................................              761,467,719     1,393,367,866
    Class B shares.......................................................                4,607,293         5,485,204
  Dividends reinvested:
    Class A shares.......................................................                9,436,692        11,495,460
    Class B shares.......................................................                   98,257             4,177
  Cost of shares redeemed:
    Class A shares.......................................................             (833,812,984)   (1,478,086,875)
    Class B shares.......................................................               (9,251,959)          (14,611)
                                                                                         ---------         ---------
      Increase (Decrease) in Net Assets from Beneficial Interest Transactions          (67,454,982)      (67,748,779)
                                                                                         ---------         ---------
        Total Increase (Decrease) in Net Assets..........................              (67,475,182)      (67,774,053)
NET ASSETS:
  Beginning of Period....................................................              395,629,700       463,403,753
                                                                                         ---------         ---------
  End of Period..........................................................         $    328,154,518  $    395,629,700
                                                                                         =========         =========








SEE 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.

                                                                                    Class A Shares
                                                                 ----------------------------------------------------
                                                                                 Year Ended July 31,
                                                                 ----------------------------------------------------
PER SHARE DATA:                                                  1997        1996        1995        1994        1993
                                                                 ----        ----        ----        ----        ----
<S>                                                           <C>         <C>         <C>         <C>         <C>
    Net asset value, beginning of period.........             $  1.00     $  1.00     $  1.00     $  1.00     $  1.00
                                                                 ----        ----        ----        ----        ----
    Investment Operations:
    Investment income-net........................                .029        .029        .031        .023        .024
                                                                 ----        ----        ----        ----        ----
    Distributions:
    Dividends from investment income-net.........               (.029)      (.029)      (.031)      (.023)      (.024)
                                                                 ----        ----        ----        ----        ----
    Net asset value, end of period...............             $  1.00     $  1.00     $  1.00     $  1.00     $  1.00
                                                                 ====        ====        ====        ====        ====
TOTAL INVESTMENT RETURN..........................                2.95%       2.94%       3.14%       2.27%       2.46%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......                 .64%        .65%        .52%        .33%        .33%
    Ratio of net investment income
      to average net assets......................                2.91%       2.91%       3.07%       2.24%       2.43%
    Decrease reflected in above expense ratios
      due to undertakings by the Manager.........                  .-          .-         .11%        .28%        .30%
    Net Assets, end of period (000's Omitted)....            $327,226    $390,155    $463,404    $699,105    $608,534














SEE NOTES TO FINANCIAL STATEMENTS.

</TABLE>
<TABLE>
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
FINANCIAL HIGHLIGHTS (CONTINUED)
    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.

                                                                                                 Class B Shares
                                                                                         --------------------------------
                                                                                          Year Ended         Year Ended
                                                                                           July 31,           July 31,

PER SHARE DATA:                                                                              1997               1996(1)
                                                                                            ------             ------
<S>                                                                                       <C>                <C>
    Net asset value, beginning of period....................................              $  1.00            $  1.00
                                                                                              ---                ---
    Investment Operations:
    Investment income-net...................................................                     .026              .025
                                                                                              ---                ---
    Distributions:
    Dividends from investment income-net....................................                (.026)             (.025)
                                                                                              ---                ---
    Net asset value, end of period..........................................                     $  1.00           $  1.00
                                                                                              ===                ===
TOTAL INVESTMENT RETURN.....................................................                 2.61%              2.56%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.................................                 1.00%              1.00%
    Ratio of net investment income
      to average net assets.................................................                 2.52%              2.45%
    Decrease reflected in above expense ratios
      due to undertakings by the Manager....................................                  .07%               .08%
    Net Assets, end of period (000's Omitted)...............................                 $928             $5,475
    (1)  From August 1, 1995 (commencement of initial offering) to July 31, 1996.











SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
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") is the distributor
of the Fund's shares, which are sold to the public without a sales load. The
Fund is authorized to issue an unlimited number of $.001 par value shares in
the following classes of shares: Class A and Class B. Class A shares and
Class B shares are identical except for 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-1under the Act
and, 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 1% of
the value of the average daily net assets of Class B shares.
    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 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.
    (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 $174,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to July 31, 1997. The
carryover does not include net realized securities losses from November 1,
1996 through July 31, 1997 which are treated for Federal income tax purposes,
as arising in fiscal 1998. If not applied, $8,000 of the carryover expires in
fiscal 2002, $114,000 expires in fiscal 2003, $33,000 expires in fiscal 2004
and $19,000 expires in fiscal 2005.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    At July 31, 1997, 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 that if in any full fiscal year the aggregate expenses of the Fund,
exclusive of taxes, brokerage, interest on borrowings and extraordinary
expenses, exceed 11\2% of the value of the Fund's average net assets, the
Fund may deduct from payments to be made to the Manager, or the Manager will
bear such excess expense. There was no expense reimbursement during the
period ended July 31, 1997.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, 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 period ended July 31, 1997, $7,812 was charged
to the Fund pursuant to the Class B Distribution Plan.
    (C) Under 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 average daily net
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 period ended July 31, 1997, the Fund was charged an aggregate of
$217,509 pursuant to the Class A Shareholder Services Plan.
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), 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 in respect of their
services. The Distributor determines the amounts to be paid to Service
Agents.
    The Manager has undertaken through January 31, 1998, that if the
aggregate expenses of Class B of the Fund (exclusive of taxes, brokerage,
interest on borrowings and extraordinary expenses) 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 Class B Shareholder Services Plan to the
extent of any excess expense and up to the full fee payable under such Plan.
During the period ended July 31, 1997, $11,719 was charged to the Fund
pursuant to the Class B Shareholder Services Plan, of which $2,734 was
reimbursed by the Manager.
    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 $114,834 during the period ended July 31, 1997.
    (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, 1997, 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 and financial highlights. Our procedures included
confirmation of securities owned as of July 31, 1997 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, 1997,
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 3, 1997

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, 1997 as "exempt-interest dividends" (not subject to regular Federal and
for individuals who are California residents, California personal income
taxes).



Registration Mark
[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.                        573/699AR977
Registration Mark
[Dreyfus logo]
General California
Municipal Money
Market Fund
Annual Report
July 31, 1997























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