GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1999-02-05
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YEAR 2000 ISSUES (UNAUDITED)

  The  fund  could  be  adversely  affected  if the computer systems used by The
Dreyfus  Corporation  and  the  fund' s  other service providers do not properly
process  and  calculate date-related information from and after January 1, 2000.
The  Dreyfus  Corporation  is working to avoid Year 2000-related problems in its
systems  and  to  obtain  assurances  from other service providers that they are
taking  similar  steps.  In  addition,  issuers  of securities in which the fund
invests may be adversely affected by Year 2000-related problems. This could have
an impact on the value of the fund's investments and its share price.

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 12-month period ended November 30, 1998 as shown in
the following table:

                                                     YIELD     EFFECTIVE YIELD*
                                                    _______     _____________

   Class A Shares   . . . . . . . . . . . . .         2.74%         2.77%

   Class B Shares   . . . . . . . . . . . . .         2.37%         2.39%

ECONOMY

  During  1998,  the  main  regions  of  the  world  had very different economic
fundamentals.  The  U.S.  began  the  period  with  a  strong  economy near full
employment, with unemployment only slightly above 4%. The tight labor market led
the  Federal  Reserve Board to contemplate a rise in interest rates early in the
year.  The  U.S.  economy  cooled enough over the months that the Fed decided to
stand  pat.  Evidence  of  economic  cooling continued to accumulate and worries
about  the  world economy intensified. Financial stresses pushed the Fed to ease
beginning  in September. After many years of subpar economic growth, continental
Europe  moved  into a sustained economic expansion. The overall European economy
benefited  as  interest  rates  in  peripheral countries such as Spain and Italy
fell,  approaching  the  lower  levels  established  by  Germany,  on the eve of
currency unification. Unlike the U.S., Europe has substantial excess capacity of
productive  plants and labor. In Asia, weak economies were pervasive as a result
of  the  Asian  financial  crisis.  The Latin American economies weakened as the
financial stresses spread throughout that region.

  A  main  influence  on  the  U.S.  economy this year was the foreign financial
crisis  and cooling of the world economy. The positive effects hit first. Actual
inflation  and  expected  inflation  dropped,  causing  a  decline  in long-term
Treasury bond yields and mortgage rates. This caused a boom in housing. The drop
in inflation helped the consumer sector as more of the growth in consumer income
was  left  over  after  inflation to buy goods and services. Consumers benefited
from a combination of good growth in real income, a strong labor market and past
increases in the prices of assets they owned.

  The  negative  effect of Asian weakness was felt in the industrial sector more
than  the  consumer  sector.  Corporate  profits weakened, especially in sectors
affected  by  the Asian crisis such as world-traded commodities (oil, metals and
paper) and exports. One result of the industrial weakness was to cool off a U.S.
economy that had been growing rapidly.

  The  major  change  in  the  economic  outlook  over  recent months has been a
downward  shift  in  expectations  for  world  economic  growth. A credit crunch
developed in emerging countries and former communist countries, sharply reducing
the  economic  outlook  for  Asia  and  Latin  America  as well as for commodity
exporting  countries throughout the world. The effect on Europe and the U.S. has
been to lower expectations of profit growth and drive down bond yields. Monetary
policy has begun to ease in both the U.S. and Europe.

  Evidence  of  a  weaker  world  economy  accumulated as the financial stresses
continued.  A  worsened financial crisis occurred between the Russian default in
mid-August  and  the  fallout  from  the Long-Term Capital Management hedge fund
crisis  through  early October. However, proactive steps were taken to stabilize
the  Japanese  banks,  design  a  support  package  for Brazil and ease monetary
policy.  There  appears to be a shift in the priorities of key policymakers from
fighting potential inflation to restimulating future world economic growth.

MARKET ENVIRONMENT/PORTFOLIO OVERVIEW

  The  manner in which the Federal Reserve eased this past quarter was a gradual
process.  For  three  successive months, beginning in September, the Fed reduced
the  target  rate for Fed Funds a total of 75 basis points. The Fed also lowered
the  Discount  Rate by 25 basis points each, in November and December. The Fed's
actions provided even greater strength to an already strong short-term municipal
money  market.  Prior to these rate cuts, the short-term market had already felt
the  effects  of  the diminished supply of eligible new issuance over the summer
months.  This  year' s  summer calendar of municipal notes (consisting mainly of
California  paper)  was  drastically reduced by a combination of factors. Due to
the strength of local and state economies, several issuers reduced the amount of
short-term  borrowing  needed.  Additionally,  many  issuers came to market with
securities with maturities beyond the 13-month maximum restriction allowable for
tax-exempt  money  funds.  Other  issues were converted to a shortened synthetic
structure,  thus  eliminating the ability to extend out into the one-year range.
This  reduction in supply resulted in lower yields for most one-year paper, both
national and state specific.

We extended your Fund's average maturity to the 50-day and over range in early
summer,  just  prior  to  the market strengthening. Your Fund benefited from our
purchase of securities in the one-year range at yields significantly higher than
what  is  currently  available  in  the market. As the summer progressed, yields
began  to drop as they reflected the diminished supply of one-year notes. During
this  period  we  utilized  the  commercial  paper market to maintain the Fund's
average  maturity.  As year-end approaches, we will continue to search for those
longer-term  investment  opportunities  which  will  lock  in higher rates while
providing an attractive return to the California tax-exempt investor. As always,
we  will  structure  the portfolio in an attempt to maximize current yield while
maintaining our commitment to high quality tax-exempt investments.

               Very truly yours,



               [Richard J. Moynihan signature]


               Richard J. Moynihan

               Director, Municipal Portfolio Management

               The Dreyfus Corporation

December 15, 1998

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                                    NOVEMBER 30, 1998

                                                                                                  Principal

Tax Exempt Investments--103.0%                                                                     Amount            Value
- -------------------------------------------------------                                        ______________    ______________
<S>                                                                                            <C>               <C>
California--94.7%

Alameda County, TRAN 4.50%, 7/7/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $    5,000,000    $    5,025,932

Alameda County Industrial Development Authority, Revenue, VRDN

 (Spectrum Label Corp.)

  3.20%, Series A (LOC; Wells Fargo Bank) (a)  . . . . . . . . . . . . . . . . . . . . . .          4,000,000         4,000,000

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

  3.40% (LOC; National Bank of Canada) (a) . . . . . . . . . . . . . . . . . . . . . . . .          8,850,000         8,850,000

California Health Facilities Finance Authority, Revenue, VRDN, (Catholic Health
Care):

    2.75%, Series D (Insured; MBIA and Liquidity Facility; Rabobank Nederland) (a) . . . .         10,400,000        10,400,000

    2.75%, VRDN (Insured; MBIA and Liquidity Facility; Rabobank Nederland) (a).  . . . . .          5,815,000         5,815,000

California Pollution Control Financing Authority,

 PCR, Refunding (Pacific Gas and Electric):

    2.85%, Series B (LOC; Rabobank Nederland) (a)  . . . . . . . . . . . . . . . . . . . .          6,400,000         6,400,000

    2.70%, Series A (LOC; Swiss Bank Corp.) (a)  . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

    3.35%, Series B (LOC; Deutsche Bank) (a) . . . . . . . . . . . . . . . . . . . . . . .          6,700,000         6,700,000

    3.25%, Series C (LOC; Kredietbank) (a) . . . . . . . . . . . . . . . . . . . . . . . .         17,000,000        17,000,000

  RRR, Refunding (Ultra Power Rocklin Project)

    3.20%, Series A (LOC; Bank of America) (a) . . . . . . . . . . . . . . . . . . . . . .          7,600,000         7,600,000

  SWDR

    (Colmac Energy Project) 2.70%, Series A (LOC; Swiss Bank Corp.) (a)  . . . . . . . . .          6,500,000         6,500,000

California School Cash Reserve Program Authority,

  4.50%, Series A, 7/2/99 (Insured; AMBAC) . . . . . . . . . . . . . . . . . . . . . . . .         10,000,000        10,042,717

State of California:

  4.125%, Series BJ, 6/1/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         13,000,000        13,008,809

  CP 2.90%, 1/15/99 (LOC: Morgan Guaranty Trust Co., Bayerische Landesbank,

    Credit Suisse, Landesbank Hessen Tharige and Westdeutsche Landesbank). . . . . . . . .          9,000,000         9,000,000

  RAN 4%, 6/30/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         15,000,000        15,071,910

California Statewide Community Development Authority,

 Multi-Family Revenue, VRDN (Canyon Creek Apartments)

  2.85%, Series C (Corp. Guaranty; FNMA) (a) . . . . . . . . . . . . . . . . . . . . . . .         11,800,000        11,800,000

California Transit Finance Authority, VRDN 3.05% (BPA; Credit Suisse and Insured; FSA) (a).. .      6,000,000         6,000,000

City of Camarillo, MFHR, VRDN (Heritage Park)

  2.75%, Series A (Corp. Guaranty; FNMA) (a) . . . . . . . . . . . . . . . . . . . . . . .          6,600,000         6,600,000

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

  3.25% (LOC; Wells Fargo Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .          7,300,000         7,300,000

Dublin Housing Authority, MFHR, VRDN (Park Sierra)

  2.75%, Series A (LOC; Kredietbank) (a).  . . . . . . . . . . . . . . . . . . . . . . . .          4,400,000         4,400,000

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

  2.75% (LOC; Wells Fargo Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

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

  2.95%, Series A (LOC; Wells Fargo Bank) (a)  . . . . . . . . . . . . . . . . . . . . . .          3,100,000         3,100,000

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

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998

                                                                                                  Principal

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

California (continued)

Irwindale, IDR, VRDN (Toys R Us Inc. Project)

  3.52% (LOC; Bankers Trust Co.) (a).  . . . . . . . . . . . . . . . . . . . . . . . . . .     $    3,000,000    $    3,000,000

Kern County Board of Education, TRAN 4.25%, 6/30/99. . . . . . . . . . . . . . . . . . . .          9,000,000         9,032,486

Los Angeles, MFHR, VRDN:

  (Beverly Park Apartments) 3%, Series A (LOC; Chase Manhattan Bank) (a) . . . . . . . . .          9,600,000         9,600,000

  (Loans To Lender Program) 3.20%, Series B (LOC; Federal Home Loan Banks) (a) . . . . . .          8,900,000         8,900,000

Los Angeles County, TRAN 4.50%, Series A, 6/30/99. . . . . . . . . . . . . . . . . . . . .         15,000,000        15,069,300

Los Angeles County Metropolitan Transportation Authority,

 Sales Tax Revenue, Refunding, VRDN

  2.80%, Series A (Insured; MBIA and Liquidity Facility; Credit Locale de France) (a)  . .         11,000,000        11,000,000

M-S-R Public Power Agency California, VRDN (San Juan Project)

  3.25%, Series F (LOC; FNB Chicago and Insured; MBIA) . . . . . . . . . . . . . . . . . .          3,000,000         3,000,000

Newport Beach, Revenues, VRDN:

  3.25%, Series A (Hoag Member Hospital) (a) . . . . . . . . . . . . . . . . . . . . . . .          5,500,000         5,500,000

  3.25%, Series B (Hoag Member Hospital) (a).  . . . . . . . . . . . . . . . . . . . . . .          5,500,000         5,500,000

Oakland Joint Powers Financing Authority, Lease Revenues

  3.15%, Series A, (LOC; Commerzbank and Insured; FSA) (a) . . . . . . . . . . . . . . . .          5,000,000         5,000,000

Orange County, Apartment Development Revenue, Refunding, VRDN

  (Villa La Paz) 2.75%, Series F (LOC; FNMA) (a) . . . . . . . . . . . . . . . . . . . . .         11,500,000        11,500,000

  (Wlco LF) 2.90%, Series G, (LOC; FNMA) (a).  . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

San Bernardino County, COP, Refunding, VRDN

 (Medical Center Financing Project)

  2.95%, (LOC; Landesbank Hessen and Insured; MBIA) (a). . . . . . . . . . . . . . . . . .          9,500,000         9,500,000

San Jose, MFHR, VRDN:

  (Fairway Glen) 2.80%, Series A (LOC; FGIC and Insured; FGIC) (a) . . . . . . . . . . . .          3,500,000         3,500,000

  (Sienna at Renaissance Square Apartments)

    2.95%, Series A (LOC; Key Bank of Washington) (a) .  . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

Santa Cruz County Board of Education, TRAN 4%, 6/30/99 . . . . . . . . . . . . . . . . . .          5,000,000         5,008,898

Simi Valley, MFHR, VRDN (Shadowridge Apartments)

  2.80% (LOC; Citibank) (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          8,000,000         8,000,000

University of California, Board of Regents, Revenues, CP:

 4%, 12/10/98 (LOC; Bank of America, Bank of Montreal, Canadian Imperial Bank of

    Commerce, Credit Agricole and Societe Generale)  . . . . . . . . . . . . . . . . . . .          6,000,000         6,000,000

  3.15%, 1/26/99 (LOC; Bank of America, Bank of Montreal, Canadian Imperial Bank of

    Commerce, Credit Agricole and Societe Generale)  . . . . . . . . . . . . . . . . . . .          7,500,000         7,500,000

Wateruse Financing Authority, California Revenues, VRDN

  2.60%, (LOC; Credit Suisse and Insured; FSA) (a).  . . . . . . . . . . . . . . . . . . .         15,000,000        15,000,000

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

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998

                                                                                                  Principal

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

U.S. Related--8.3%

Commonwealth of Puerto Rico:

 Government Development Bank, Refunding, VRDN

    2.90%, Series A (LOC; Credit Suisse and Insured; MBIA) (a).  . . . . . . . . . . . . .     $    6,000,000    $    6,000,000

  TRAN 3.50%, Series A, 7/30/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         12,000,000        12,050,400

Commonwealth of Puerto Rico Highway and Transportation Authority,

 Transportation Revenue, VRDN

  2.75%, Series A (LOC; Bank of Nova Scotia and Insured; AMBAC) (a). . . . . . . . . . . .         10,700,000        10,700,000

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $354,975,452). . . . . . . . . . . . . . . . . . . . . . . . . . .             103.0%      $354,975,452
                                                                                                      =======     =============

LIABILITIES, LESS CASH AND RECEIVABLES . . . . . . . . . . . . . . . . . . . . . . . . . .              (3.0%)    $ (10,489,696)
                                                                                                      =======     =============

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%      $344,485,756
                                                                                                      =======     =============

Summary of Abbreviations
- -----------------------------------------------------------------------------

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

Summary of Combined Ratings (Unaudited)
- -----------------------------------------------------------------------------

Fitch                or            Moody's             or            Standard & Poor's              Percentage of Value
____                               ________                          _________________              ___________________

F1+/F1                             VMIG1/MIG1, P1                    SP1+/SP1, A1+/A1                     93.9%

AAA/AA (b)                         Aaa/Aa (b)                        AAA/AA (b)                            2.5

Not Rated (c)                      Not Rated (c)                     Not Rated (c)                         3.6

                                                                                                       _______

                                                                                                         100.0%
                                                                                                       =======

Notes to Statement of Investments:
- -----------------------------------------------------------------------------

(a) Securities payable  on  demand. Variable interest rate-subject to periodic
    change.

(b) Notes which  are not F, MIG or SP rated are represented by bond ratings of
    the issuers.

(c) 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.

(d) At November  30,  1998,  the  Fund  had  $98,550,000 (28.6% 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                         NOVEMBER 30, 1998

                                                                                                    Cost              Value
                                                                                                _____________     _____________
<S>                                                                                              <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $354,975,452      $354,975,452

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                            2,015,342

                                 Prepaid expenses and other assets . . . . . . . . . . . .                                9,649
                                                                                                                  _____________

                                                                                                                    357,000,443
                                                                                                                  _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                              148,758

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                                  855

                                 Cash overdraft due to Custodian . . . . . . . . . . . . .                              256,986

                                 Payable for investment securities purchased . . . . . . .                           12,050,400

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               57,688
                                                                                                                  _____________

                                                                                                                     12,514,687

                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $344,485,756
                                                                                                                  =============


REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                         $344,689,379

                                 Accumulated net realized gain (loss) on investments . . .                             (203,623)
                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $344,485,756
                                                                                                                  =============

                                                  NET ASSET VALUE PER SHARE
                                    ________________________________________________________

                                                                                                  Class A            Class B
                                                                                                _____________     _____________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $335,726,122        $8,759,634

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        335,929,505         8,759,874

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 NOVEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                              <C>                <C>
INCOME                      Interest Income  . . . . . . . . . . . . . . . . . . . . . . .                          $12,104,536

EXPENSES:                   Management fee--Note 2(a)  . . . . . . . . . . . . . . . . . .       $  1,794,867

                            Shareholder servicing costs--Note 2(c) . . . . . . . . . . . .            301,613

                            Registration fees  . . . . . . . . . . . . . . . . . . . . . .             64,431

                            Professional fees  . . . . . . . . . . . . . . . . . . . . . .             52,089

                            Custodian fees . . . . . . . . . . . . . . . . . . . . . . . .             38,041

                            Trustees' fees and expenses--Note 2(d) . . . . . . . . . . . .             25,611

                            Prospectus and shareholders' reports . . . . . . . . . . . . .             17,183

                            Distribution fees (Class B)--Note 2(b) . . . . . . . . . . . .             14,052

                            Miscellaneous  . . . . . . . . . . . . . . . . . . . . . . . .             11,160

                                                                                                 ____________

                                   Total Expenses  . . . . . . . . . . . . . . . . . . . .          2,319,047

                            Less--reduction in shareholder servicing costs

                                due to undertaking--Note 2(c)  . . . . . . . . . . . . . .             (4,897)

                                                                                                 ____________

                                   Net Expenses  . . . . . . . . . . . . . . . . . . . . .                            2,314,150

                                                                                                                   ____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                            9,790,386

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . . . . . .                               (8,381)

                                                                                                                   ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . . . . . .                         $  9,782,005

                                                                                                                   ============


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

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

STATEMENT OF CHANGES IN NET ASSETS

                                                               Year Ended           Four Months Ended          Year Ended

                                                            November 30, 1998      November 30, 1997*         July 31, 1997
                                                          ___________________     ___________________    ___________________

<S>                                                          <C>                      <C>                        <C>
OPERATIONS:

  Investment income--net . . . . . . . . . . . . . . . .      $    9,790,386          $    3,677,244             $10,680,146

  Net realized gain (loss) on investments  . . . . . . .              (8,381)                 (1,369)                (20,200)

                                                               _____________           _____________           _____________

       Net Increase (Decrease) in Net Assets

         Resulting from Operations . . . . . . . . . . .           9,782,005               3,675,875              10,659,946
                                                               _____________           _____________           _____________

DIVIDENDS TO SHAREHOLDERS FROM:

 Investment income--net:

    Class A shares . . . . . . . . . . . . . . . . . . .          (9,626,016)             (3,654,371)            (10,581,881)

    Class B shares . . . . . . . . . . . . . . . . . . .            (164,370)                (22,873)                (98,265)
                                                               _____________           _____________           _____________

       Total Dividends . . . . . . . . . . . . . . . . .          (9,790,386)             (3,677,244)            (10,680,146)
                                                               _____________           _____________           _____________

BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):

 Net proceeds from shares sold:

    Class A shares . . . . . . . . . . . . . . . . . . .         820,634,796             342,614,076             761,467,719

    Class B shares . . . . . . . . . . . . . . . . . . .          57,212,398               5,520,599               4,607,293

  Dividends reinvested:

    Class A shares . . . . . . . . . . . . . . . . . . .           8,929,793               3,367,363               9,436,692

    Class B shares . . . . . . . . . . . . . . . . . . .             162,222                  22,219                  98,257

  Cost of shares redeemed:

    Class A shares . . . . . . . . . . . . . . . . . . .        (854,932,309)           (312,104,246)           (833,812,984)

    Class B shares . . . . . . . . . . . . . . . . . . .         (51,283,460)             (3,802,463)             (9,251,959)
                                                               _____________           _____________           _____________
       Increase (Decrease) in Net Assets from

         Beneficial Interest Transactions  . . . . . . .        (19,276,560)              35,617,548             (67,454,982)
                                                               _____________           _____________           _____________

           Total Increase (Decrease) in Net Assets . . .        (19,284,941)              35,616,179             (67,475,182)

NET ASSETS:

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

  End of Period  . . . . . . . . . . . . . . . . . . . .        $344,485,756            $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>
<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
                                                     ______________________________________________________________________

                                                                    Four Months Ended

                                                      Year Ended       November 30,             Year Ended July 31,
                                                                                       ____________________________________

PER SHARE DATA:                                    November 30, 1998      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  . . . . . . . . . . ..          .027               .010          .029      .029       .031      .023
                                                        _______            _______       _______   _______    _______   _______

   Distributions:

   Dividends from investment income--net . . . .          (.027)             (.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. . . . . . . . . . . . .           2.78%              2.96%(2)      2.95%     2.94%      3.14%     2.27%

RATIOS/SUPPLEMENTAL DATA:

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

   Ratio of net investment income

       to average net assets . . . . . . . . . .           2.74%              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) . .       $335,726           $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.

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

                                                         November 30,            Four Months Ended          Year Ended July 31,

                                                                                                           __________________

PER SHARE DATA:                                              1998              November 30, 1997(1)          1997        1996(2)
                                                       ________________        ___________________          ______       ______

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

   Investment Operations:

   Investment income--net  . . . . . . . . . . . .              .024                      .009                .026         .025
                                                              ______                    ______              ______       ______

   Distributions:

   Dividends from investment income--net . . . . .             (.024)                    (.009)              (.026)       (.025)
                                                              ______                    ______              ______       ______

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

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . .              2.39%                     2.57%(3)            2.61%        2.56%

RATIOS/SUPPLEMENTAL DATA:

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

   Ratio of net investment income

       to average net assets . . . . . . . . . . .              2.34%                     2.62%(3)            2.52%        2.45%

   Decrease reflected in above expense ratios

       due to undertakings by the Manager  . . . .               .07%                      .13%(3)             .07%         .08%

   Net Assets, end of period (000's Omitted) . . .            $8,760                    $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

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

   General  California  Municipal  Money  Market Fund (the "Fund") is registered
under  the  Investment  Company  Act  of  1940,  as  amended  (the  "Act") as a
non-diversified  open-end  management  investment company. The Fund's investment
objective  is  to  maximize  current  income  exempt  from  Federal and State of
California  income  taxes  to  the  extent  consistent  with the preservation of
capital   and  the  maintenance  of  liquidity.  The  Dreyfus  Corporation  (the
"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
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 custody agreement,
the  Fund  received  net  earnings  credits  of  $20,722 during the period ended
November  30,  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 of 1986, as
amended (the "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 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 $204,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if  any,  realized subsequent to November 30, 1998. If not
applied, $8,200

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

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

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, $21,000 expires
in fiscal 2005 and $9,000 expires in fiscal 2006.

At November 30, 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  November 30, 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 November 30, 1998, Class B shares were
charged $14,052 pursuant to the Distribution Plan.

   (C)  Under  the  Shareholder  Services Plan with respect to Class A ("Class A
Shareholder   Services   Plan"), Class  A  shares  reimburse  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 Class A shares and providing reports and other information,
and  services  related  to  the  maintenance of shareholder accounts. During the
period ended November 30, 1998, Class A shares were charged $141,357 pursuant to
the Class A Shareholder Services Plan.

   Under  the  Shareholder  Services  Plan  with  respect  to Class B ("Class B
Shareholder  Services  Plan"), Class B shares pay the Distributor, at an annual
rate of .25 of 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.

   The  Manager  had undertaken through November 30, 1998, that if the aggregate
expenses  of  Class  B  shares  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 November
30, 1998, Class B shares were charged $21,077, of which $4,897 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  November  30, 1998, the Fund was charged $13,800 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.

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  November 30, 1998, and the related statement of operations
for the year then ended and the statement of changes in net assets 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 November 30, 1998 by correspondence with the custodian
and brokers. 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 November 30, 1998, the results
of its operations for the year then ended, and the changes in its net assets and
the  financial  highlights  for  each of the indicated years, in conformity with
generally accepted accounting principles.


                                      [ERNST & YOUNG LLP SIGNATURE LOGO]


New York, New York
January 4, 1999



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 November
30, 1998 as "exempt-interest dividends" (not subject to regular Federal and, for
individuals who are California residents, California personal income taxes).


                                   [reg.tm 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.                                         573/699AR9811

General California

Municipal Money

Market Fund

Annual Report

November 30, 1998



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