GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1997-03-27
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General California
Municipal Money
Market Fund
Semi-Annual
Report
January 31, 1997
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Letter to Shareholders
Dear Shareholder:
    We are pleased to report the performance for General California Municipal
Money Market Fund for its semi-annual reporting period ended January 31, 1997
as shown in the following table:
                                                           Annualized
                              Annualized Yield           Effective Yield*
                              ----------------           ----------------
   Institutional Shares            5.25%                      5.38%
   Class A Shares                  2.87%                      2.91%
   Class B Shares                  2.53%                      2.56%
THE ECONOMY
    In recent months, the U.S. economy appeared to be advancing more rapidly
than it had been previously, as incoming data reflected an accelerated pace.
December's strong gains in non-farm payrolls and the length of the workweek,
along with upward revisions of both for November, convinced many analysts
that fourth quarter Gross Domestic Product (GDP) growth would be strong _ in
the 4% range. Their estimates were, in actuality, low, as the reported GDP
rate was a brisk 4.7%. While such strong economic growth has not yet produced
higher inflation, forthcoming data on wage and benefits growth, home sales,
and purchasing managers' outlays may rekindle inflation concerns. Some
Federal Reserve Board (the "Fed") officials have been voicing concern
already, although Fed Chairman Greenspan gave little sense of urgency in his
commentary to the Senate Budget Committee on January 21. Additionally, the
Fed Beige Book survey of national economic conditions contained few hints of
price pressures.
    Given these indications, the Fed seems likely to rely on anti-inflation
rhetoric rather than action until evidence of price pressures becomes more
persuasive. Nonetheless, words of caution from Fed Chairman Alan Greenspan
during December, and January's robust economic data, have pushed up market
interest rates on six-month to one-year money market securities, as investors
begin to see the possibility of higher rates ahead.
MARKET/PORTFOLIO OVERVIEW
    The economic picture is always an important component of our overall
portfolio strategy. However, market expectations can also affect the
short-term municipal market_as was the case in this most recent period. The
anticipation of Federal Reserve activity prior to the Presidential election
this past November left the market jittery, while the lack of Fed action in
the weeks following the election helped settle the market into a trading
range. However, various other influences which affect our market (most
specifically supply/demand) can lead us to adjust our strategy, and result in
a portfolio structure and/or average maturity which may not appear to
coincide exactly with interest rate moves, economic conditions, or forecasts.
For example, during this period, one might have expected that your Fund's
average maturity would be relatively short in expectation of higher rates.
However, we were comfortable extending the average maturity beyond 50 days,
and locking in attractive rates as 1996 drew to a close, due to the
expectation of limited availability of high quality municipal note issues in
early 1997. This strategy served us well when rates dropped significantly
(albeit temporarily) in January, and also leaves flexibility to extend
further should conditions warrant and opportunities arise. However, in the
California market specifically, our ability to maintain your Fund's average
maturity in the 50-day range was hampered by the lack of high quality
one-year California issues. Such maturities are in high demand by California
money funds since the preponderance of California note issues mature in late
June and early July. As an alternative, the commercial paper market provided
an opportunity to match the yields available in the one-year range; however,
the average maturity was shortened slightly in the process.
    In the coming months, we expect additional technical market situations to
occur such as increased redemptions due to tax payments during April and the
maturation of significant note issues in June. As a result of these
anticipated market
events, we expect to adjust the Portfolio's composition to respond to the
supply and cash flow changes in an effort to maximize your Fund's yield
performance. As we endeavor to accomplish this, we will continue to commit to
those issues which meet our high quality investment guidelines and which
provide the appropriate level of liquidity for your Fund's needs.
Additionally, we will monitor those conditions which affect our marketplace
and adjust our investment policy where necessary in seeking to enhance your
Fund's performance.
    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we appreciate greatly your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Very truly yours,

                          (RICHARD J. MOYNIHAN SIGNATURE LOGO)
                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
February 17, 1997
New York, N.Y.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly. Yield fluctuates and past performance is no guarantee of
future results.
<TABLE>
<CAPTION>


GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Investments                                                                          January 31, 1997 (Unaudited)
                                                                                                   Principal
Tax-Exempt Investments_100.0%                                                                        Amount          Value
                                                                                                  ____________  ______________
California_93.0%
<S>                                                       <C>                <C>                <C>             <C>
Alameda County, TRAN 4.50%, 6/30/97.........................................                    $    6,500,000  $   6,514,034
Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)
  3.45% (LOC; National Bank of Canada) (a,b)................................                         8,850,000      8,850,000
California Housing Finance Agency:
  Home Mortgage Revenue
    4%, Series J, 7/24/97 (GIC; FGIC).......................................                        14,000,000     14,000,000
  Multi-Family Revenue, Refunding, VRDN
    3.45%, Series B (Corp. Guaranty; FNMA) (a)..............................                         5,600,000      5,600,000
California Pollution Control Financing Authority:
  PCR, Refunding (Pacific Gas and Electric):
    CP 3.40%, Series E, 3/12/97 (LOC; Morgan Guaranty Trust Co.) (b)........                        10,000,000    10,000,000
    VRDN 3.45%, Series B (LOC; Rabobank Nederland) (a,b)....................                         5,000,000     5,000,000
  VRDN:
    Refunding
      (Ultra Power Malaga Project) 3.65%, Series B (LOC; Bank of America) (a,b)                      5,500,000      5,500,000
    RRR:....................................................................
      (Delano Project) 3.65% (LOC; ABN-Amro Bank) (a,b).....................                         5,500,000      5,500,000
    SWDR (Colmac Energy Project) 3.50%, Series A (LOC; Swiss Bank Corp.) (a,b)                       6,500,000      6,500,000
California School Cash Reserve Program Authority, Notes
  4.75%, Series A, 7/2/97 (Insured; MBIA)...................................                        14,000,000     14,058,329
State of California, RAN:
  3.40%, Series C-1, 6/30/97 (Liquidity Facility: Bank of America,
    Bank of Nova Scotia, Commerzbank and National Westminster Bank).........                         14,500,000    14,500,000
  3.50%, Series C-3, 6/30/97 (Liquidity Facility: Bank of America,
    Bank of Nova Scotia, Commerzbank and National Westminster Bank).........                         10,000,000    10,000,000
California Statewide Community Development Authority, VRDN:
  Apartment Development Revenue, Refunding
    3.50%, Series A-7 (Corp. Guaranty; FNMA) (a)............................                         6,500,000      6,500,000
  Multi-Family Revenue (Canyon Creek Apartments)
    3.55%, Series C (Corp. Guaranty; FNMA) (a)..............................                         11,800,000    11,800,000
City of Camarillo, MFHR, VRDN (Heritage Park)
  3.55%, Series A (Corp. Guaranty; FNMA) (a)................................                         6,800,000      6,800,000
City of Clovis, MFHR, VRDN (Fowler Place Apartments Project)
  3.25% (LOC; Wells Fargo Bank) (a,b).......................................                         7,500,000      7,500,000
Fresno, MFHR, Refunding, VRDN (Heron Pointe Apartments)
  3.45% (LOC; First Interstate Bank of California) (a,b)....................                         5,300,000      5,300,000
Golden Empire Schools Financing Authority, VRDN (Kern High School District)
  3.45% (LOC: Canadian Imperial Bank of Commerce and National Westminster Bank) (a,b)                7,200,000      7,200,000
City of Hayward Housing Authority, Multi-Family Revenue, Refunding, VRDN
  (Barrington Hills) 3.45%, Series A (Corp. Guaranty; FNMA)(a)..............                        13,550,000     13,550,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Investments (continued)                                                             January 31, 1997 (Unaudited)
                                                                                                 Principal
Tax-Exempt Investments (continued)                                                                Amount          Value
                                                                                               ______________   _____________
California (continued)
Huntington Beach, MFHR, VRDN:
  (Five Points Seniors Project)
    3.45%, Series A (LOC; Wells Fargo Bank) (a,b)...........................                    $    3,100,000  $   3,100,000
  (Mercury Savings and Loan Village)
    4.55%, Series A (LOC; Resolution Funding Corp.) (a,b)...................                         6,000,000      6,000,000
Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.675% (LOC; Bankers Trust) (a,b)                    3,000,000      3,000,000
City of Los Angeles, TRAN 4.50%, 6/19/97....................................                         6,000,000      6,011,352
Los Angeles, MFHR, VRDN:
  (Beverly Park Apartments) 3.30%, Series A (LOC; Chase Manhattan Bank) (a,b)                        9,600,000      9,600,000
  (Loans To Lender Program):
    3.65%, Series A (LOC; Federal Home Loan Banks) (a,b)....................                         2,300,000      2,300,000
    3.65%, Series B (LOC; Federal Home Loan Banks) (a,b)....................                         7,500,000      7,500,000
  (Lucas Studios Project) 3.60%, Series D (LOC; Bank of America) (a,b)......                         3,655,000      3,655,000
  (Oakwood Apartments) 3.60%, Series B (LOC; Sumitomo Bank) (a,b)...........                         9,555,000      9,555,000
Los Angeles County:
  Pension Obligation, Refunding, VRDN
    3.40%, Series C (Insured; AMBAC and Liquidity Facility; Bank of Nova Scotia) (a)                 8,000,000      8,000,000
  TRAN 4.50%, 6/30/97 (LOC: Credit Suisse, Bank of America, Morgan Guaranty
Trust Co.,
    Union Bank of Switzerland and WestDeutsche Landesbank) (b)..............                        25,500,000     25,571,325
Los Angeles County Metropolitan Transportation Authority, Sales Tax Revenue,
Refunding
  VRDN 3.45%, Series A (Insured; MBIA and Liquidity Facility; Credit Locale  de France) (a)         16,100,000     16,100,000
Metropolitan Water District, Water Works Revenue, Refunding, VRDN
  3.45%, Series A (Insured; AMBAC and LOC; ABN-Amro Bank) (a,b).............                        10,200,000     10,200,000
Oakland Unified School District, TRAN 4.25%, 10/14/97.......................                         8,000,000      8,020,176
Olcese Water District, COP, CP (Rio Bravo Water Delivery System Program)
  3.60%, Series A, 2/18/97 (LOC; Sumitomo Bank) (b).........................                         8,800,000      8,800,000
Ontario Redevelopment Agency, Revenue, VRDN (Mission Oaks)
  3.70%, Series A (LOC; Union Bank of California) (a,b).....................                         5,270,000      5,270,000
Sacramento County Housing Authority, MFHR, VRDN (Stone Creek Apartments
Project)
  3.65%, Series L (LOC; First Interstate Bank of California) (a,b)..........                         5,450,000      5,450,000
San Bernardino County, COP, VRDN 3.65% (LOC; Sumitomo Bank) (a,b)...........                        12,000,000     12,000,000
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
  (French Co. Project) 3.55% (LOC; Credit Commercial de France) (a,b).......                         3,800,000      3,800,000
San Francisco City and County Redevelopment Agency, Multi-Family Revenue,
VRDN
  (Bayside Village Project) 3.50%, Series B (LOC; Industrial Bank of Japan) (a,b)                    4,500,000      4,500,000
San Jose, MFHR, VRDN (Sienna at Renaissance)
  3.60%, Series A (LOC; Bank One of Arizona) (a,b)..........................                         5,000,000      5,000,000
Southern California Public Power Authority, Revenue, Refunding, VRDN
  (Southern Transmission) 3.40% (Liquidity Facility; Swiss Bank Corp. and
    LOC; AMBAC) (a,b).......................................................                         6,000,000      6,000,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Investments (continued)                                                            January 31, 1997 (Unaudited)
                                                                                                   Principal
Tax-Exempt Investments (continued)                                                                   Amount          Value
                                                                                                -------------    -----------
U.S. Related_7.0%
Commonwealth of Puerto Rico, TRAN 4%, Series A, 7/30/97.....................                    $    7,000,000  $   7,017,900
Commonwealth of Puerto Rico Government Development Bank, CP:
  3.55%, 2/6/97.............................................................                        10,000,000     10,000,000
  3.55%, 3/12/97............................................................                         8,316,000      8,316,000
                                                                                                                ______________
TOTAL INVESTMENTS (cost $359,439,116).......................................                                     $359,439,116
                                                                                                                 =============
Summary of Abbreviations
AMBAC      American Municipal Bond Assurance Corporation    MBIA   Municipal Bond Investors Assurance
COP        Certificate of Participation                               Insurance Corporation
CP         Commercial Paper                                 MFHR    Multi-Family Housing Revenue
FGIC       Financial Guaranty Insurance Company             PCR     Pollution Control Revenue
FNMA       Federal National Mortgage Association            RAN     Revenue Anticipation Notes
GIC        Guaranteed Investment Contract                   RRR     Resources Recovery Revenue
IDR        Industrial Development Revenue                   SWDR    Solid Waste Disposal Revenue
LOC        Letter of Credit                                 TRAN    Tax and Revenue Anticipation Notes
                                                            VRDN    Variable Rate Demand Notes

Summary of Combined Ratings
Moody's                             or                Standard & Poor's                      Percentage of Value
- --------                                              ------------------                     -------------------
VMIG1/MIG1, P1 (c)                                    SP1+/SP1, A1+/A1 (c)                          91.8%
Aaa/Aa (d)                                            AAA/AA (d)                                     5.5
Not Rated (e)                                         Not Rated (e)                                  2.7
                                                                                                   --------
                                                                                                   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 January 31, 1997, 52.9% of the
   Fund's net assets are backed by letters of credit issued by domestic
   banks, foriegn banks and government agencies.
    (c)  P1 and A1 are the highest ratings assigned tax exempt commercial
   paper by Moody's and Standard & Poor's, respectively.
    (d)  Notes which are not MIG or SP rated are represented by bond ratings
   of the issuers.
    (e)  Securities which, while not rated by Moody's and Standard & Poor's,
   respectively, have been determined by the Manager to be of comparable
   quality to those rated securities in which the Fund may invest.
    (f)  At January 31, 1997, the Fund had $141,830,000 (38.9% of net assets)
   invested in securities whose payment of prinicipal and interest is
   dependent upon revenues generated from housing projects.


See notes to financial statements.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Assets and Liabilities                                                                January 31, 1997 (Unaudited)
                                                                                                      Cost             Value
                                                                                                _______________   ________________
ASSETS:                          Investments in securities_See Statement of Investments           $359,439,116      $359,439,116
                                 Cash.......................................                                           2,488,561
                                 Interest receivable........................                                           2,777,385
                                 Prepaid expenses and other assets..........                                              31,487
                                                                                                                    ______________
                                                                                                                     364,736,549
                                                                                                                    ______________
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates                                           187,900
                                 Due to Distributor.........................                                               2,486
                                 Accrued expenses and other liabilities.....                                             105,092
                                                                                                                    ______________
                                                                                                                         295,478
                                                                                                                    ______________
NET ASSETS..................................................................                                        $364,441,071
                                                                                                                    ==============
REPRESENTED BY:                  Paid-in capital............................                                        $364,609,588
                                 Accumulated net realized gain (loss) on investments                                   (168,517)
                                                                                                                    ______________
NET ASSETS..................................................................                                        $364,441,071
                                                                                                                    ==============

                                                NET ASSET VALUE PER SHARE
                                                -------------------------
                                                                                                  Class A            Class B
                                                                                               _____________      _____________
Net Assets..................................................................                   $359,290,733      $  5,150,338
Shares Outstanding..........................................................                    359,459,331         5,150,257
NET ASSET VALUE PER SHARE...................................................                          $1.00             $1.00
                                                                                                     ======             ======




See notes to financial statements.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Operations                                                        Six Months Ended January 31, 1997 (Unaudited)
INVESTMENT INCOME
INCOME                           Interest Income............................                                       $6,894,595
EXPENSES:                        Management fee_Note 2(a)...................                    $   968,274
                                 Shareholder servicing costs_Note 2(c)......                        256,821
                                 Professional fees..........................                         24,282
                                 Custodian fees.............................                         22,469
                                 Trustees' fees and expenses_Note 2(d)......                         13,606
                                 Registration fees..........................                         12,356
                                 Prospectus and shareholders' reports.......                          7,578
                                 Distribution fees (Class B)_Note 2(b)......                          5,714
                                 Miscellaneous..............................                          8,463
                                                                                                  ----------
                                       Total Expenses.......................                       1,319,563
                                 Less-reduction in shareholder servicing costs due to
                                     undertaking-Note 2(c)..................                         (2,494)
                                                                                                   _________
                                       Net Expenses.........................                                        1,317,069
                                                                                                                    ---------
INVESTMENT INCOME_NET.......................................................                                        5,577,526
NET REALIZED GAIN (LOSS) ON INVESTMENTS_Note 1(b)...........................                                            5,156
                                                                                                                   ___________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                       $5,582,682
                                                                                                                   ===========

SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Statement of Changes in Net Assets
                                                                                         Six Months Ended
                                                                                         January 31, 1997        Year Ended
                                                                                           (Unaudited)          July 31, 1996
                                                                                         _________________      _____________
OPERATIONS:
  Investment income_net..................................................                 $    5,577,526        $   12,788,844
  Net realized gain (loss) on investments................................                          5,156               (25,274)
                                                                                            ____________        _____________
      Net Increase (Decrease) in Net Assets Resulting from Operations....                      5,582,682            12,763,570
                                                                                            ____________        _____________
DIVIDENDS TO SHAREHOLDERS FROM:
  Investment income_net:
    Class A shares.......................................................                     (5,505,071)         (12,784,667)
    Class B shares.......................................................                        (72,455)              (4,177)
                                                                                            ____________        _____________
      Total Dividends....................................................                     (5,577,526)         (12,788,844)
                                                                                            ____________        _____________
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold:
    Class A shares.......................................................                    339,502,366        1,393,367,866
    Class B shares.......................................................                      2,271,333            5,485,204
  Dividends reinvested:
    Class A shares.......................................................                      4,943,578           11,495,460
    Class B shares.......................................................                         72,447                4,177
  Cost of shares redeemed:
    Class A shares.......................................................                   (375,315,216)      (1,478,086,875)
    Class B shares.......................................................                     (2,668,293)             (14,611)
                                                                                            ____________        _____________
      Increase (Decrease) in Net Assets from Beneficial Interest Transactions                (31,193,785)         (67,748,779)
                                                                                            ____________        _____________
        Total Increase (Decrease) in Net Assets..........................                    (31,188,629)         (67,774,053)
NET ASSETS:
  Beginning of Period....................................................                    395,629,700          463,403,753
                                                                                            ____________        _____________
  End of Period..........................................................               $    364,441,071      $   395,629,700
                                                                                            ============        ==============

</TABLE>

SEE NOTES TO FINANCIAL STATEMENTS.

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.
<TABLE>
<CAPTION>


                                                                               Class A Shares
                                                       ------------------------------------------------------------------------
                                                        Six Months Ended
                                                        January 31, 1997                   Year Ended July 31,
                                                                               ------------------------------------------------
PER SHARE DATA:                                           (Unaudited)            1996      1995     1994      1993     1992
                                                       ---------------           -----      ----    ----      ----     -----
    <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                .029      .031     .023      .024      .036
                                                           -------               -----      ----    ----      ----     -----
    Distributions:
    Dividends from investment income_net..                   (.015)              (.029)    (.031)   (.023)    (.024)    (.036)
                                                           -------               -----      ----    ----      ----     -----
    Net asset value, end of period........                 $  1.00             $  1.00   $  1.00  $  1.00   $  1.00   $  1.00
                                                          =========            ========  =======  =======  ========  ========
TOTAL INVESTMENT RETURN...................                    2.90%*              2.94%     3.14%    2.27%     2.46%     3.65%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets                    .67%*               .65%      .52%     .33%      .33%      .20%
    Ratio of net investment income
      to average net assets...............                    2.88%*              2.91%     3.07%    2.24%     2.43%     3.59%
    Decrease reflected in above expense ratios
      due to undertakings by the Manager..                    --                   --        .11%     .28%      .30%      .41%
    Net Assets, end of period (000's Omitted)             $359,291            $390,155  $463,404 $699,105  $608,534  $549,383
    *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
                                                                                    _________________________________________
                                                                                       Six Months Ended
                                                                                       January 31, 1997         Year Ended
PER SHARE DATA:                                                                           (Unaudited)        July 31, 1996(1)
                                                                                    --------------------     ----------------
    Net asset value, beginning of period................................                    $  1.00                $  1.00
                                                                                            --------               -------
    Investment Operations:
    Investment income_net...............................................                       .013                   .025
                                                                                            --------               -------
    Distributions:
    Dividends from investment income_net................................                      (.013)                 (.025)
                                                                                            --------               -------
    Net asset value, end of period......................................                    $  1.00                $  1.00
                                                                                          ==========             =========
TOTAL INVESTMENT RETURN.................................................                       2.56%(2)               2.56%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.............................                       1.00%(2)               1.00%
    Ratio of net investment income
      to average net assets.............................................                       2.54%(2)               2.45%
    Decrease reflected in above expense ratios
      due to undertakings by the Manager................................                        .09%(2)                .08%
    Net Assets, end of period (000's Omitted)...........................                     $5,150                 $5,475
    (1)  From August 1, 1995 (commencement of initial offering) to July 31, 1996.
    (2)  Annualized.

</TABLE>
SEE NOTES TO FINANCIAL STATEMENTS.

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") 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 1% of the value of the average daily net assets of Class B.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so. There is no
assurance, however, that the Fund will be able to maintain a stable net asset
value per share of $1.00.
    The Fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management
estimates and assumptions. Actual results could differ from those estimates.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Trustees to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Interest income, adjusted
for amortization of premiums and original issue discounts on investments, is
earned from settlement date and recognized on the accrual basis. Realized
gain and loss from securities transactions are recorded on the identified
cost basis. Cost of investments represents amortized cost.
    The Fund follows an investment policy of investing primarily in municipal
obligations of one state. Economic changes affecting the state and certain of
its public bodies and municipalities may affect the ability of issuers within
the state to pay interest on, or repay principal of, municipal obligations
held by the Fund.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain are normally declared and paid
annually, but the Fund may make distributions on a more frequent basis to
comply with the distribution requirements of the Internal Revenue Code. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)
    The Fund has an unused capital loss carryover of approximately $155,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to July 31, 1996. The
carryover does not include net realized securities losses from November 1,
1995 through July 31, 1996 which are treated for Federal income tax purposes,
as arising in fiscal 1997. If not applied, $8,200 of the carryover expires in
fiscal 2002, $113,800 expires in fiscal 2003 and $33,000 expires in fiscal 2004.
    At January 31, 1997, the cost of investments for Federal income tax
purposes was substantially the same as the cost for financial reporting
purposes (see the Statement of Investments).
NOTE 2_MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the value
of the Fund's average daily net assets and is payable monthly. The Agreement
provides that if in any full fiscal year the aggregate expenses of the Fund,
exclusive of taxes, brokerage, interest on borrowings and extraordinary
expenses, exceed 11\2% of the value of the Fund's average net assets, the
Fund may deduct from payments to be made to the Manager, or the Manager will
bear such excess expense. There was no expense reimbursement pursuant to the
Agreement during the period ended January 31, 1997.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, the Fund
directly bears the cost of preparing, printing and distributing prospectuses
and statements of additional information and of implementing and operating
the Class B Distribution Plan. In addition, the Fund reimburses the Distributor
for payments made to third parties for distributing Class B shares at an
aggregate annual rate  of up to .20 of 1% of the value of the average daily
net assets of Class B. During the period ended January 31, 1997, $5,714 was
charged to the Fund pursuant to the Class B Distribution Plan.
    (C) Under the Fund's Shareholder Services Plan with respect to Class A
("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus Service
Corporation, a wholly-owned subsidiary of the Manager, an amount not to
exceed an annual rate of .25 of 1% of the value of the average daily net
assets of Class A for certain allocated expenses of providing personal
services and/or maintaining shareholder accounts. The services provided may
include personal services relating to shareholder accounts, such as answering
shareholder inquiries regarding the Fund and providing reports and other
information, and services related to the maintenance of shareholder accounts.
During the period ended January 31, 1997, the Fund was charged an aggregate
of $158,172 pursuant to the Class A Shareholder Services Plan.
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), the Fund pays the Distributor at an annual rate
of .25 of 1% of the value of the average daily net assets of Class B for the
provision of certain services. The services provided may include personal
services relating to shareholder accounts, such as answering shareholder
inquiries regarding the Fund and providing reports and other information, and
services related to the maintenance of shareholder accounts. The Distributor
may make payments to Service Agents in respect of these services. The
Distributor determines the amounts to be paid to Service Agents.
    The Manager has currently undertaken through July 31, 1997, that if the
aggregate expenses of Class B of the Fund (exclusive of certain expenses as
described above) exceed 1% of the value of the average daily net assets of
Class B, the Manager will reimburse the expenses of the Fund under the Class
B Shareholder Services Plan to the extent of any excess expense and up to the
full fee payable under the Class B Shareholder Services Plan. During the
period ended January 31, 1997, $8,571 was charged to the Fund pursuant to the
Class B Shareholder Services Plan, of which $2,494 was reimbursed by the
Manager.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)
    The Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of
the Manager, under a transfer agency agreement for
providing personnel and facilities to perform transfer agency services for
the Fund. Such compensation amounted to $8,502 during the period ended
January 31, 1997.
    (D) Each trustee who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $250
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.

Registration Mark
Registration Mark
(DREYFUS LION D LOGO)
GENERAL CALIFORNIA
MUNICIPAL MONEY MARKET FUND
200 Park Avenue
New York, NY 10166
MANAGER
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166
CUSTODIAN
The Bank of New York
90 Washington Street
New York, NY 10286
TRANSFER AGENT &
DIVIDEND DISBURSING AGENT
Dreyfus Transfer, Inc.
P.O. Box 9671
Providence, RI 02940

Printed in U.S.A.                                                573/699SA971
(DREYFUS LOGO)




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