GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1998-08-07
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[Dreyfus lion "d" logo]                                    (reg.tm)

[Dreyfus logo]
                                   (reg.tm)

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.                                          573/699SA985

General California

Municipal Money

Market Fund

Semi-Annual

Report

May 31, 1998




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 the six-month period ended May 31, 1998 as shown in the
following table:

                                        ANNUALIZED                 ANNUALIZED
                                         YIELD                 EFFECTIVE YIELD*
                                        __________             ________________

        Class A Shares                   2.93%                       2.97%

        Class B Shares                   2.57%                       2.60%

Money Market Overview

Over the past several months, mixed economic signals have made it difficult to
discern the direction in which the economy is moving.  Consumer spending
increased 0.5% in both April and May, fueled by both strong employment and
income growth. In addition, construction spending also rose 0.8% in April for
the fifth straight monthly increase. On the other hand, spring housing data was
mixed, with new home sales rising to record levels in April and existing-home
sales and new housing starts dropping off. The U.S. trade gap also continued to
widen, as manufacturers reported declines in exports to Asia, and tough
competition from cheaper Asian imports.  With arguments to be made for both
continued growth and emerging weakness, it appears that Federal Reserve Board
monetary policy will remain on hold at least until something major happens to
sway Board members' opinions one way or another.

  Inflation has remained benign throughout the period. Incoming data from April
did show a small 0.2% increase in the Consumer Price Index, although this modest
rise was the largest in six months. With no consensus as to the direction of the
economy, the Federal Reserve Board Open Market Committee left short-term
interest rates unchanged at its May meeting; however, the decision to do so may
not have been unanimous.  Those most wary of inflation may win out in upcoming
meetings if the economy does not cool on its own. Interest rates on money market
securities  fluctuated modestly during the period, but remained largely
unchanged.  As U.S. Treasury borrowing needs continued to reduce the supply of
money market securities, demand remained steady.

Market Environment/Portfolio Overview

  While the Fed has remained quiet over the past six months, market technicals
(i.e. supply/demand fluctuations) have played a major role in our overall
investment  strategy.  The municipal money market has experienced some of these
changes in seasonal cash flows  and note issuance since our last report.  For
example, in late December, the short-term municipal market experienced a sharp,
albeit temporary, rise in short-term rates as a result of corporate seasonal
window dressing.  Dealers priced securities at attractive levels in order to
minimize their inventories, which helped to boost your Fund's yield at year
end. The situation reversed in January as assets flowed back into the tax-
exempt money funds, thereby  putting downward pressure on yields.  During this
period, yields on tax-exempt money market funds fluctuated in response to
these supply and demand imbalances.

  By mid-January, the market stabilized and normal trading patterns, for
the most  part, returned and continued through March. In April, money funds
were tapped for income tax payments which, once again, put upward pressure on
rates as funds experienced redemptions.  Supply conditions in late May
reversed this trend as municipal fund managers anticipated the effect of over
$10 billion notes leaving the market when they  mature this month.

  Unlike previous summer financing periods, this year's calendar of
municipal notes appropriate for purchase for your Fund was drastically
reduced by a combination of factors. Due to the strength of local and state
economies, many issuers (a significant number of which were California-exempt)
reduced the amount of short-term borrowings.  Additionally, many issuers came
to market with maturities outside of the 13-month maximum maturity allowable
for money funds, whereas these notes were eligible for purchase in prior years.
Other issues were converted to a synthetic structure that is not currently
permitted for purchase in your Fund.  The overall result was a lower yield for
those note issues that were considered appropriate investments for your
Fund. We expect to choose selectively among these issues and those to
follow in the coming weeks to structure the portfolio in an attempt to
maximize  current  yield while maintaining our commitment to high quality tax-
exempt investments.

  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 this Fund and in The
Dreyfus Corporation.

               Very truly yours,


               [Richard J. Moynihan signature logo]


               Richard J. Moynihan

               Director, Municipal Portfolio Management

               The Dreyfus Corporation

June 18, 1998

New York, N.Y.

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

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                             MAY 31, 1998 (UNAUDITED)

                                                                                                   Principal
Tax Exempt Investments--100.0%                                                                      Amount           Value
- -------------------------------------------------------                                          ______________   ______________
<S>                                                                                             <C>              <C>
California--94.3%

Alameda County, Industrial Development Authority, Revenue, VRDN (Spectrum Label
Corp.)

  3.90%, Series A (LOC; Wells Fargo Bank) (a,b)............................................    $    4,000,000    $    4,000,000

Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)

  3.85% (LOC; National Bank of Canada) (a,b)...............................................         8,850,000         8,850,000

State of California, RAN 4.50%, 6/30/98....................................................         7,450,000         7,454,313

California Economic Development Financing Authority, Revenue, VRDN

 (California Independent Systems Project):

    3.70%, Series C (LOC; Bank of America) (a,b)...........................................         5,000,000         5,000,000

    3.75%, Series B (LOC; Bank of America) (a,b)...........................................        13,500,000        13,500,000

California Health Facilities Finance Authority, Revenue, VRDN:

 (Catholic Health Care)

    3.75%, Series D (Insured; MBIA and Liquidity Facility; Rabobank Nederland) (a).........        10,400,000        10,400,000

  Refunding (Sutter/CHS)

    3.75%, Series C (LOC; Rabobank Nederland) (a,b)........................................         7,000,000         7,000,000

California Housing Finance Agency, Home Mortgage Revenue

  3.95%, Series J, 8/3/98 (Insured; FGIC)..................................................        12,210,000        12,210,000

California Pollution Control Financing Authority:

 PCR, Refunding:

   (Pacific Gas and Electric):

       CP 3.45%, Series D, 8/18/98 (LOC; Union Bank of Switzerland) (b)....................         6,000,000         6,000,000

       VRDN:

         3.70%, Series B (LOC; Rabobank Nederland) (a,b)...................................         5,000,000         5,000,000

         3.75%, Series A (LOC; Swiss Bank Corp.) (a,b).....................................        10,000,000        10,000,000

         3.85%, Series B (LOC; Deutsche Bank) (a,b)........................................        7,000,000         7,000,000

  VRDN:

    RRR, Refunding (Ultra Power Rocklin Project)

       3.85%, Series A (LOC; Bank of America) (a,b)........................................         7,600,000         7,600,000

    SWDR:

       (Colmac Energy Project) 3.75%, Series A (LOC; Swiss Bank Corp.) (a,b)...............         6,500,000         6,500,000

       (Shell Martinez Refining) 3.75%, Series A (Corp. Guaranty; Shell Oil Co.) (a).......         2,000,000         2,000,000

       (Taormina Industries Project) 4.35%, Series B (LOC; Sanwa Bank) (a,b)...............        11,795,000        11,795,000

California Statewide Community Development Authority:

 Multi-Family Revenue, VRDN (Canyon Creek Apartments)

    3.75%, Series C (Corp. Guaranty; FNMA) (a).............................................        11,800,000        11,800,000

  TRAN 4.50%, Series A, 6/30/98 (Insured; FSA and LOC; California Statewide) (b)...........        10,000,000        10,005,354

California Transit Finance Authority, VRDN 3.85% (BPA; Credit Suisse and Insured; FSA) (a).         6,000,000         6,000,000

City of Camarillo, MFHR, VRDN (Heritage Park)

  3.70%, Series A (Corp. Guaranty; FNMA) (a)...............................................         6,700,000         6,700,000

City of Clovis, MFHR, VRDN (Fowler Place Apartments Project)

  3.70% (LOC; Wells Fargo Bank) (a,b)......................................................         7,300,000         7,300,000

Fresno, MFHR, Refunding, VRDN (Heron Pointe Apartments)

  3.70% (LOC; Wells Fargo Bank) (a,b)......................................................         5,100,000         5,100,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                 MAY 31, 1998 (UNAUDITED)

                                                                                                  Principal
Tax Exempt Investments (continued)                                                                 Amount             Value
- -------------------------------------------------------                                         ______________     ______________

California (continued)

Huntington Beach, MFHR, VRDN (Five Points Seniors Project)

  3.75%, Series A (LOC; Wells Fargo Bank) (a,b)............................................    $    3,100,000    $    3,100,000

Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.825% (LOC; Bankers Trust Co.) (a,b)......         3,000,000         3,000,000

Los Angeles, MFHR, VRDN:

  (Beverly Park Apartments) 3.75%, Series A (LOC; Chase Manhattan Bank) (a,b)..............         9,600,000         9,600,000

  (Loans To Lender Program) 3.85%, Series B (LOC; Federal Home Loan Banks) (a,b)...........         7,500,000         7,500,000

  (Oakwood Apartments) 4.50%, Series B (LOC; Sumitomo Bank) (a,b)..........................        14,305,000        14,305,000

Los Angeles County, TRAN 4.50%, Series A, 6/30/98..........................................        21,000,000        21,011,806

Los Angeles County Metropolitan Transportation Authority, Sales Tax Revenue,
Refunding

  VRDN 3.70%, Series A (Insured; MBIA and Liquidity Facility; Credit Locale de France) (a).        11,100,000        11,100,000

Metropolitan Water District of Southern California, Water Works Revenue,
Refunding, VRDN

  3.70%, Series A (Insured; AMBAC and LOC; ABN-Amro Bank) (a,b)............................        10,200,000        10,200,000

Oakland Unified School District of Alameda County, TRAN 4.25%, 10/28/98....................        13,425,000        13,447,379

Olcese Water District, COP, CP (Rio Bravo Water Delivery System Program)

  4.10%, Series A, 7/21/98 (LOC; Sumitomo Bank) (b)........................................         8,400,000         8,400,000

Ontario Redevelopment Agency, Revenue, VRDN (Mission Oaks)

  4.05%, Series A (LOC; Union Bank of California) (a,b)....................................         5,770,000         5,770,000

San Diego County, TRAN 4.50%, 9/30/98 (LOC: Bank of Nova Scotia,

  Canadian Imperial Bank of Commerce and Commerz Bank) (b).................................         7,000,000         7,015,554

San Francisco City and County Redevelopment Agency, Multi-Family Revenue, VRDN

  (Bayside Village Project) 4.20%, Series B (LOC; Industrial Bank of Japan) (a,b)..........         4,500,000         4,500,000

San Jose, MFHR, VRDN (Sienna at Renaissance Square Apartments)

  3.80%, Series A (LOC; Key Bank of Washington) (a,b)......................................         5,000,000         5,000,000

Simi Valley, MFHR, VRDN (Shadowridge Apartments) 3.60% (LOC; Citibank) (a,b)...............         8,000,000         8,000,000

University of California, Board of Regents, Revenues, CP

 3.50%, 8/12/98 (LOC: Bank of America, Bank of Montreal,
 Canadian Imperial Bank of Commerce,

  Credit Agricole and Societe Generale) (b)................................................        10,000,000        10,000,000

U.S. Related--5.7%

Commonwealth of Puerto Rico:

  Government Development Bank, CP 3.70%, 7/17/98...........................................        10,000,000        10,000,000

  TRAN 4.50%, Series A, 7/30/98............................................................         9,000,000         9,011,341

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $332,175,747)......................................................                        $332,175,747

                                                                                                                  =============
</TABLE>

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

Summary of Abbreviations
- -----------------------------------------------------------------------------
<S>         <C>                                                     <C>         <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                                        PCR         Pollution Control Revenue

FGIC        Financial Guaranty Insurance Company                    RAN         Revenue Anticipation Notes

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
</TABLE>

<TABLE>
<CAPTION>


Summary of Combined Ratings (Unaudited)
- -----------------------------------------------------------------------------
Fitch (c)            or            Moody's             or            Standard & Poor's              Percentage of Value
_______                            ________                          _________________              ___________________
<S>                                <C>                               <C>                                  <C>
F1+/F1                             VMIG1/MIG1, P1 (d)                SP1+/SP1, A1+/A1 (d)                 93.9%

AAA/AA (e)                         Aaa/Aa (e)                        AAA/AA (e)                            2.3

Not Rated (f)                      Not Rated (f)                     Not Rated (f)                         3.8
                                                                                                         ______
                                                                                                         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 May 31, 1998, 63.0% 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 investments.

(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 May 31, 1998, the Fund had $109,735,000 (32.7% 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>
<CAPTION>


GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                  MAY 31, 1998 (UNAUDITED)

                                                                                                    Cost             Value
                                                                                                _____________     _____________
<S>                              <C>                                                             <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments...      $332,175,747      $332,175,747
                                 Interest receivable.......................................                           3,690,001
                                 Prepaid expenses and other assets.........................                              29,940
                                                                                                                  _____________
                                                                                                                    335,895,688
                                                                                                                  _____________
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates.............                             181,626
                                 Due to Distributor........................................                                 495
                                 Cash overdraft due to Custodian...........................                             461,807
                                 Accrued expenses..........................................                              52,075
                                                                                                                   _____________
                                                                                                                        696,003
                                                                                                                  _____________
NET ASSETS.................................................................................                        $335,199,685
                                                                                                                  =============
REPRESENTED BY:                  Paid-in capital...........................................                        $335,400,904
                                 Accumulated net realized gain (loss) on investments.......                           (201,219)
                                                                                                                  _____________
NET ASSETS.................................................................................                        $335,199,685
                                                                                                                  =============
</TABLE>

                               NET ASSET VALUE PER SHARE
                              _____________________________
<TABLE>
<CAPTION>

                                                                                                 Class A           Class B
                                                                                                _____________     _____________
<S>                                                                                              <C>                 <C>
Net Assets                                                                                       $327,989,800        $7,209,885

Shares Outstanding                                                                                328,190,839         7,210,065
NET ASSET VALUE PER SHARE                                                                               $1.00             $1.00
                                                                                                        =====             =====

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS             SIX MONTHS ENDED MAY 31, 1998 (UNAUDITED)
INVESTMENT INCOME
<S>                         <C>                                                                   <C>                <C>
INCOME                      Interest Income................................................                          $6,429,154
EXPENSES:                   Management fee--Note 2(a)......................................       $   897,326
                            Shareholder servicing costs--Note 2(c).........................           166,200
                            Professional fees..............................................            44,000
                            Registration fees..............................................            34,150
                            Custodian fees.................................................            18,766
                            Trustees' fees and expenses--Note 2(d).........................            12,503
                            Prospectus and shareholders' reports...........................             7,905
                            Distribution fees (Class B)--Note 2(b).........................             5,255
                            Miscellaneous..................................................             6,581
                                                                                                  ___________
                                   Total Expenses..........................................         1,192,686
                            Less--reduction in shareholder servicing costs
                                due to undertaking--Note 2(c)..............................           (2,578)
                                                                                                  ___________
                                   Net Expenses............................................                           1,190,108
                                                                                                                    ___________
INVESTMENT INCOME--NET.....................................................................                           5,239,046

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b).........................................                             (5,977)
                                                                                                                    ___________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS.......................................                          $5,233,069
                                                                                                                    ===========


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

<TABLE>
<CAPTION>



GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                             Six Months Ended
                                                               May 31,1998          Four Months Ended         Year Ended
                                                               (Unaudited)         November 30, 1997*        July 31, 1997
                                                          ___________________     ___________________    ___________________
<S>                                                           <C>                    <C>                       <C>
OPERATIONS:

  Investment income--net...............................       $    5,239,046         $     3,677,244           $  10,680,146

  Net realized gain (loss) on investments..............               (5,977)                 (1,369)                (20,200)
                                                               _____________           _____________           _____________

       Net Increase (Decrease) in Net Assets
         Resulting from Operations.....................            5,233,069               3,675,875              10,659,946
                                                                _____________           _____________           _____________

DIVIDENDS TO SHAREHOLDERS FROM:
 Investment income--net:
    Class A shares.....................................          (5,169,969)             (3,654,371)            (10,581,881)
    Class B shares.....................................             (69,077)                (22,873)                (98,265)
                                                               _____________           _____________           _____________

       Total Dividends.................................          (5,239,046)             (3,677,244)            (10,680,146)
                                                               _____________           _____________           _____________

BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
 Net proceeds from shares sold:
    Class A shares.....................................          369,385,968             342,614,076             761,467,719
    Class B shares.....................................           27,422,770               5,520,599               4,607,293
Dividends reinvested:
    Class A shares.....................................            4,808,946               3,367,363               9,436,692
    Class B shares.....................................               67,309                  22,219                  98,257
  Cost of shares redeemed:
    Class A shares.....................................         (407,301,300)           (312,104,246)           (833,812,984)
    Class B shares.....................................          (22,948,728)             (3,802,463)             (9,251,959)
                                                               _____________           _____________           _____________

       Increase (Decrease) in Net Assets from

         Beneficial Interest Transactions..............         (28,565,035)              35,617,548             (67,454,982)

                                                               _____________           _____________           _____________

           Total Increase (Decrease) in Net Assets.....          (28,571,012)             35,616,179             (67,475,182)

NET ASSETS:

  Beginning of Period..................................          363,770,697             328,154,518             395,629,700
                                                               _____________           _____________           _____________

  End of Period........................................         $335,199,685            $363,770,697            $328,154,518
                                                               =============           =============           =============

- -----------------------------
* The Fund changed its fiscal year end from July 31 to November 30.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------
<TABLE>
<CAPTION>

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
                                                  ______________________________________________________________________________

                                                   Six Months Ended  Four Months Ended
                                                     May 31, 1998       November 30,             Year Ended July 31,
                                                                                       ________________________________________

PER SHARE DATA:                                       (Unaudited)         1997(1)        1997      1996      1995       1994
                                                   _______________  _____________   ________   ________   ________   ________
   <S>                                                 <C>             <C>          <C>         <C>       <C>       <C>
   Net asset value, beginning of period...........     $  1.00         $    1.00    $    1.00  $   1.00   $   1.00  $    1.00
                                                       _______         _________    _________  _________  _________  ________

   Investment Operations:
   Investment income--net.........................         .015             .010         .029      .029       .031       .023
                                                       _______         _________    _________  _________  _________  ________
   Distributions:

   Dividends from investment income--net..........       (.015)            (.010)       (.029)     (.029)     (.031)    (.023)
                                                       _______         _________    _________  _________  _________  ________

   Net asset value, end of period.................     $  1.00         $    1.00    $    1.00  $    1.00  $    1.00  $   1.00
                                                       =======         =========    =========  =========  =========  =========

TOTAL INVESTMENT RETURN...........................     2.95%(2)           2.96%(2)       2.95%      2.94%      3.14%     2.27%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets........      .66%(2)            .70%(2)        .64%       .65%       .52%      .33%

   Ratio of net investment income
       to average net assets......................     2.92%(2)           2.97%(2)       2.91%       2.91%     3.07%     2.24%

   Decrease reflected in above expense ratios
       due to undertakings by the Manager.........       --                 --             --          --       .11%      .28%

   Net Assets, end of period (000's Omitted)...... $327,990           $361,102       $327,226    $390,155  $463,404  $699,105
- -----------------------------

(1)  The Fund changed its fiscal year end from July 31 to November 30.
(2)  Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</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.
<TABLE>
<CAPTION>

                                                                               Class B Shares
                                                       ________________________________________________________________

                                                       Six Months Ended
                                                         May 31, 1998           Four Months Ended         Year Ended July 31,
                                                                                                         __________________

PER SHARE DATA:                                           (Unaudited)          November 30, 1997(1)        1997        1996(2)
                                                       ________________        ___________________        ______       ______
   <S>                                                     <C>                       <C>                 <C>          <C>

   Net asset value, beginning of period...........         $  1.00                   $  1.00             $  1.00      $  1.00
                                                            ______                    ______              ______       ______

   Investment Operations:
   Investment income--net.........................            .013                      .009                .026         .025
                                                            ______                    ______              ______       ______

   Distributions:

   Dividends from investment income--net..........           (.013)                    (.009)              (.026)       (.025)
                                                            ______                    ______              ______       ______

   Net asset value, end of period.................         $  1.00                   $  1.00             $  1.00      $  1.00
                                                            ======                    ======              ======       ======

TOTAL INVESTMENT RETURN...........................            2.59%(3)                  2.57%(3)            2.61%        2.56%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets........            1.00%(3)                  1.00%(3)            1.00%        1.00%

   Ratio of net investment income
       to average net assets......................            2.63%(3)                  2.62%(3)            2.52%        2.45%

   Decrease reflected in above expense ratios
       due to undertakings by the Manager.........             .10%(3)                   .13%(3)             .07%         .08%

   Net Assets, end of period (000's Omitted)......          $7,210                    $2,669                $928       $5,475
- -----------------------------

(1)  The Fund changed its fiscal year end from July 31 to November 30.
(2)  From August 1, 1995 (commencement of initial offering) to July 31, 1996.
(3)  Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (UNAUDITED)

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  General California Municipal Money Market Fund (the "Fund") is registered
under the Investment Company Act of 1940 ("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-1 under 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 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 in securities 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.  Under the terms of the custodian agreement, the Fund
received  net  earnings  credits of $10,736 during the period ended May 31, 1998
based on  available cash balances left on deposit.  Income earned under this
arrangement is included in interest income.

  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,
<PAGE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
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NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

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 $195,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1997. If not
applied, $8,200 of the carryover expires in fiscal 2001, $113,800 expires in
fiscal  2002, $33,000 expires in fiscal 2003, $19,000 expires in fiscal 2004 and
$21,000 expires in fiscal 2005.

  At  May 31, 1998, 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, exclusive of taxes,
brokerage, interest  on borrowings and extraordinary expenses, exceed 1 1/2% 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. During the
period  ended  May  31, 1998, there was no expense reimbursement pursuant to the
Agreement.

(B) Under the Distribution Plan with respect to Class B ("Class B Distribution
Plan"), adopted  pursuant to Rule 12b-1 under the Act, Class B shares directly
bear 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, Class B shares reimburse the Distributor for
payments  made  to third parties for distributing their shares at an annual rate
up to .20 of 1% of the value of the average daily net assets of Class B. During
the period ended May 31, 1998, Class B shares were charged $5,255 pursuant to
the Distribution Plan.

  (C)  Under  the Shareholder Services Plan with respect to Class A, Class A
shares  reimburse  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 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 Class A shares and
providing reports and other information, and services related to the maintenance
of shareholder accounts.  During the period ended May 31, 1998, Class A shares
were charged $84,726 pursuant to the Shareholder Services Plan.

  Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), Class B shares pay the Distributor, at an annual
rate of .25 of 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 Class B shares and providing reports and other information,
and services related to the maintenance of shareholder accounts. The Distributor
may make payments to Service Agents in respect of their services.  The
Distributor determines the amounts to be paid to Service Agents.

<PAGE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

  The Manager had undertaken through May 31, 1998, that if the aggregate
expenses of Class B shares (exclusive of certain expenses as described above)
exceeded .80 of 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 May 31, 1998, Class B shares were
charged $7,883, of which $2,578 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.  During the period
ended May 31, 1998, the Fund was charged $43,145 pursuant to the transfer agency
agreement.

  (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.





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