GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1996-03-25
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GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the General California
Municipal Money Market Fund. For its semi-annual reporting period ended
January 31, 1996, your Fund produced an annualized yield of 3.09% per share
for Class A shares and 2.70% for Class B shares. Income dividends of
approximately $.016 per share were paid during the period for Class A shares
and $.014 for Class B shares. Reinvesting these dividends and calculating the
effect of compounding resulted in annualized effective yields of 3.13% and
2.73% for Class A shares and Class B shares, respectively.* These dividends
were exempt from Federal and State of California personal income taxes,
although some income may be subject to the Federal Alternative Minimum Tax
(AMT) for certain shareholders.**
THE ECONOMY
    On January 31, 1996, the last day of the Fund's reporting period, the
Federal Reserve Board once again lowered the Federal Funds rate another
quarter of a point to 5.25%. The Federal Funds rate is the rate of interest
that the nation's banks charge each other for overnight loans and is a key
benchmark for all other short-term interest rates. The Federal Reserve also
reduced the Discount Rate to 5.0%. The reduction in interest rates was a
continuation of the easing monetary policy of the Fed, a stance that has
prevailed since last July.
    Mounting evidence that economic growth was indeed slowing combined with
favorable inflation reports indicated that the possibility of recession
outweighed any near-term worry of a resurgence in price inflation. The
Consumer Price Index ("CPI") rose only 2.5% in 1995, the lowest rate in
nearly a decade. It also marked the fifth consecutive year that the CPI was
in the 3% or less range. The consumer sector of the economy was of increasing
concern to economic policy makers. The consumer sector comprises two thirds
of the nation's economic activity and retail sales reports in December
revealed the worst holiday season since the 1990-91 recession. Personal
income growth remained sluggish. The Conference Board, an independent
business group, reported that the Board's index of consumer confidence
declined sharply in January as consumers worried about Federal budget
negotiations and the recent flurry of layoff announcements by major
corporations.
    Industrial production was only moderate. Output of the nation's factories
crept up 0.1% in December. The annual rate of production slowed to 0.8% in
the fourth quarter of 1995, compared with 3.2% for the previous three months.
For the full calendar year, output rose 3.2%, little more than half the 5.9%
rate in 1994.
    There were strong indications that inflation was under control. If fear
of inflation was once the overriding concern of the Federal Reserve, the
focus now seems to have shifted to actions designed to avoid recession. Since
last July, the Fed has moved three times to lower interest rates. Should more
signs of economic weakness emerge, we believe that short-term interest rates
will continue to be lowered.
MARKET ENVIRONMENT
    The short-term municipal market certainly is influenced by any Federal
Reserve Board decision to lower interest rates; however, market technicals
(namely supply/demand) were the overriding factor affecting the yields that
prevailed throughout this period. By Fall, rates on short-term issues had
settled into a trading range. A steady interchange of variable rate demand
notes (VRDNs) between corporate holders and municipal money market funds kept
rates on these securities attractive, which resulted in an inverted
yield curve (rates on shorter maturities were higher than rates on longer
issues) during most of the season. Despite the Fed's easing move in early
December, its second rate reduction of the year, rates on VRDNs trended even
higher toward year-end. That was a seasonal occurrence (as prior years have
demonstrated) which reverses dramatically in January as cash returns to the
money market arena. The "January effect" leads to a high increase in demand
for VRDNs and, accordingly, a substantial yield drop on these issues as well.
The unusually large asset inflows abated by late January, thereby lessening
the high demand for VRDNs and serving to restore stability to short-term
yields.
    In previous years, the reduction of yield levels in January has been
substantial - lower rates have been sustained through most of the month and
into February. This year's drop in rates was less pronounced. We attribute
this aberration to the unresolved issues surrounding tax reform. This
uncertainty prompted remarketing agents to price VRDNs at more attractive
yields, which, of course, enhanced your Fund's overall performance.
THE PORTFOLIO
    With the inverted yield curve, daily and weekly demand notes yielded
moderately more than both commercial paper and longer-term notes through most
of the period. Our investment strategy involved lengthening the portfolio's
maturity, when possible, in order to lock in rates that we felt would
outperform variable rate notes early in 1996.
    The commercial paper and one-year note markets provided the primary means
for us to extend, while maintaining a competitive yield. However, our success
in achieving the desired average maturity was limited due to a scarcity of
high quality California-exempt issues from which to choose. As a result, your
Fund's current average maturity still leaves room to extend should we believe
a change in market or supply conditions warrant.
    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 15, 1996
New York, N.Y.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
**Income may be subject to some state and local taxes for non-California
residents.

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                         JANUARY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                        AMOUNT           VALUE
                                                                                                     _______         _______
<S>                                                                                                <C>           <C>
CALIFORNIA-91.7%
Anaheim Housing Authority, MFHR, VRDN, Refunding (Villas at Anaheim Hill)
    3.10% (LOC; National Bank of Canada) (a,b)..............................                       $ 8,850,000    $ 8,850,000
California Health Facilities Financing Authority, Revenue, VRDN:
    (Catholic Health Care)
      2.85%, Series C (Insured; MBIA and LOC; Morgan Guaranty Trust Co.) (a,b)                       5,500,000      5,500,000
    (Scirpps Memorial Hospital):
      3%, Series A (Insured; MBIA and LOC; Morgan Guaranty Trust Co.) (a,b).                         3,900,000      3,900,000
      3%, Series B (Insured; MBIA and LOC; Morgan Guaranty Trust Co.) (a,b).                        17,700,000     17,700,000
California Housing Finance Agency:
    Home Mortgage Revenue 4.60%, Series E, 2/1/96 (Insured; FGIC)...........                         5,740,000      5,740,000
    Multi-Family Revenue, Refunding, VRDN:
      2.95%, Series B (Corp. Guaranty; FNMA) (a)............................                         5,600,000      5,600,000
      2.95%, Series C (Corp. Guaranty; FNMA) (a)............................                         5,400,000      5,400,000
California Pollution Control Financing Authority:
    PCR:
      CP, Refunding (Pacific Gas and Electric):
          3.35%, Series A, 3/12/96 (LOC; Swiss Bank Corp.) (b)..............                        20,630,000     20,630,000
          3.35%, Series E, 2/12/96 (LOC; Morgan Guaranty Trust Co.) (b).....                         8,000,000      8,000,000
          3.55%, Series A, 2/16/96 (LOC; Swiss Bank Corp.) (b)..............                         5,000,000      5,000,000
      (San Diego Gas and Electric)
          4%, Series A, 9/1/96 (Corp. Guaranty; San Diego Gas and Electric).                         7,500,000      7,500,000
    VRDN:
      RRR, Refunding:
          (Ultra Power Malaga Project) 3.90%, Series B (LOC; Bank of America) (a,b)                  4,000,000      4,000,000
          (Ultra Power Rocklin Project):
            3.90%, Series A (LOC; Bank of America) (a,b)....................                         4,400,000      4,400,000
            3.90%, Series B (LOC; Bank of America) (a,b)....................                         5,100,000      5,100,000
      SWDR (Colmac Energy Project) 3.05%, 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, 7/3/96 (LOC; Industrial Bank of Japan) (b).............                         7,000,000      7,028,187
California Statewide Community Development Authority, VRDN:
    Apartment Development Revenue, Refunding:
      3.05%, Series A-7 (Corp. Guaranty; FNMA) (a)..........................                         6,500,000      6,500,000
      2.85%, Series A-6 (Corp. Guaranty; FNMA) (a)..........................                         6,400,000      6,400,000
    COP, Revenue, Refunding (Kaiser Foundation Hospital)
      2.80% (Corp. Guaranty; Kaiser Permanente) (a).........................                         7,000,000      7,000,000
    Multi-Family Revenue (Canyon Creek Apartments)
      3.35%, Series C (Corp. Guaranty; FNMA) (a)............................                        11,800,000     11,800,000
City of Camarillo, MFHR, VRDN (Heritage Park)
    3.05%, Series A (Corp. Guaranty; FNMA) (a)..............................                         6,900,000      6,900,000

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                              JANUARY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT           VALUE
                                                                                                     _______         _______
CALIFORNIA (CONTINUED)
City of Hayward Housing Authority, Multi-Family Revenue, Refunding, VRDN
    (Barrington Hills) 3.25%, Series A (Corp. Guaranty; FNMA) (a)...........                      $ 13,550,000    $13,550,000
Huntington Beach, MFHR, VRDN:
    (Five Points Seniors Project) 3.20%, Series A (LOC; Wells Fargo Bank) (a,b)                      3,100,000      3,100,000
    (Mercury Savings and Loan Village)
      4%, Series A (LOC; Resolution Funding Corp.) (a,b)....................                         6,000,000      6,000,000
Irwindale, IDR, VRDN (Toys "R" Us Inc. Project) 3.875% (LOC; Bankers Trust) (a,b)                    3,000,000      3,000,000
Kern County, TAN 4.50%, 7/2/96..............................................                         5,000,000      5,012,576
Los Angeles, MFHR, VRDN:
    (Beverly Park Apartments) 3%, Series A (LOC; Barclays Bank) (a,b).......                         9,600,000      9,600,000
    (Loans To Lender Program):
      3.95, Series A (LOC; Federal Home Loan Banks) (a,b)...................                         3,600,000      3,600,000
      3.95, Series B (LOC; Federal Home Loan Banks) (a,b)...................                         7,500,000      7,500,000
    (Lucas Studios Project) 3.40%, Series D (LOC; Bank of America) (a,b)....                         3,655,000      3,655,000
    (Oakwood Apartments) 4%, Series B (LOC; Sumitomo Bank) (a,b)............                         9,655,000      9,655,000
Los Angeles County:
    COP (Equipment Program)
      3.35%, Series A, 6/1/96 (LOC; Canadian Imperial Bank of Commerce) (b).                         7,375,000      7,375,000
    TRAN 4.50%, 7/1/96 (LOC: Bank of America, Credit Suisse,
      Morgan Guaranty Trust Co., Swiss Bank Corp., Union Bank of Switzerland
and
      West Deutsche Landesbank) (b).........................................                        20,500,000     20,568,571
Los Angeles County Metropolitan Transportation Authority,
    CP:
      Revenue 3.75%, 2/8/96 (LOC: ABN-Amro, Bank of California,
          Banque Nationale de Paris, Canadian Imperial Bank of Commerce and
          National Westminster Bank) (b)....................................                         3,900,000      3,900,000
      Sales Tax Revenue, Refunding, (Property C)
          3.30%, Series A, 3/12/96 (LOC: ABN-Amro, Bank of California,
          Banque Nationale de Paris, Canadian Imperial Bank of Commerce and
          National Westminster Bank) (b)....................................                         3,300,000      3,300,000
    VRDN:
      Revenue (General Union Station Gateway)
          2.95%, Series A (BPA; Societe Generale and Insured; FSA) (a)......                        11,000,000     11,000,000
      Sales Tax Revenue, Refunding (Property C)
          2.90%, Series A (Insured; MBIA and Liquidity Facility;
          Industrial Bank of Japan) (a,b)...................................                        21,800,000     21,800,000
Los Angeles County Transportation Commission, Sales Tax Revenue, Refunding,
VRDN
    2.90%, Series A (Insured; FGIC and Liquidity Facility; Bayerische Landesbank) (a)                6,350,000      6,350,000
Los Angeles Unified School District, TRAN 4.50%, 7/3/96.....................                        19,625,000     19,687,317

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                             JANUARY 31, 1996 (UNAUDITED)
                                                                                                   PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                  AMOUNT           VALUE
                                                                                                     _______        _______
CALIFORNIA (CONTINUED)
Paramount, MFHR, VRDN (Mercury Savings and Loan Triangle Project)
    4%, Series A (LOC; Resolution Funding Corp.) (a,b)......................                        $9,000,000    $ 9,000,000
Pleasant Hill, Multi-Family Revenue, VRDN (Brookside Apartments)
    2.95%, Series A (Corp. Guaranty; FNMA) (a)..............................                         3,000,000      3,000,000
Sacramento County Housing Authority, MFHR, VRDN (Stone Creek Apartments
Project)
    3.40%, Series L (LOC; First Interstate Bank of California) (a,b)........                         5,450,000      5,450,000
Sacramento Municipal Utility District, CP
    3.50%, Series H, 4/8/96 (LOC; Bayerische Landesbank) (b)................                         6,993,000      6,993,000
San Bernardino County:
    COP, VRDN 2.95% (LOC; Sumitomo Bank) (a,b)..............................                        12,000,000     12,000,000
    TRAN 4.50%, 7/5/96 (LOC: Bank of Nova Scotia, Banque Nationale de Paris
and
      Toronto Dominion) (b).................................................                        10,000,000     10,022,398
San Diego County, MFHR, VRDN (Country Hills Apartments)
    2.95%, Series A (Corp. Guaranty; FNMA) (a)..............................                         5,400,000      5,400,000
San Dimas Redevelopment Agency Industrial Development Authority, IDR, VRDN
    (French Co. Project) 3.70% (LOC; Credit Commercial de France) (a,b).....                         4,200,000      4,200,000
Simi Valley, MFHR, Refunding, VRDN (Creekside Village)
    3%, Series A (LOC; Bank of America) (a,b)...............................                         5,750,000      5,750,000
South Coast Education Agencies, Partnerships Pooled 5%, 8/14/96.............                        11,000,000     11,028,032
Southern Public Power Authority, Revenue, Refunding, VRDN (Transmission
Project)
    2.75% (Insured; AMBAC and LOC; Swiss Bank Corp.) (a,b)..................                         8,500,000      8,500,000
State of California Department of Water Resource, Water Systems Revenue:
    CP 3.05%, Series 1, 3/5/96 (Liquidity Facility: Canadian Imperial
       Bank of Commerce and Swiss Bank Corp.)...............................                         2,600,000      2,600,000
    VRDN (Central Valley Project)
      3.10%, Series N-V1 (LOC; Canadian Imperial Bank of Commerce) (a,b)....                        14,000,000     14,000,000
Vacaville, MFMR, VRDN (Quail Run)
    2.95%, Series A (Corp. Guaranty; FNMA) (a)..............................                         3,000,000      3,000,000
U.S. RELATED-8.3%
Commwealth of Puerto Rico Government Development Bank:
    CP:
      3.15%, 2/6/96.........................................................                         4,000,000      4,000,000
      3.75%, 2/6/96.........................................................                        10,200,000     10,200,000
      3.75%, 3/6/96.........................................................                        19,657,000     19,657,000
    Refunding, VRDN 2.85% (LOC; Credit Suisse) (a,b)........................                         4,000,000      4,000,000
                                                                                                                   __________
TOTAL INVESTMENTS (cost $456,902,081).......................................                                     $456,902,081
                                                                                                                 ============
</TABLE>

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND

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

</TABLE>

<TABLE>
<CAPTION>

SUMMARY OF COMBINED RATINGS (UNAUDITED)
MOODY'S                             OR                STANDARD & POOR'S                               PERCENTAGE OF VALUE
- -------                                               ------------------                              --------------------
<S>                                                   <C>                                                  <C>
VMIG1/MIG1, P1 (c)                                    SP1+/SP1, A1+/A1 (c)                                  93.0%
Aaa/Aa (d)                                            AAA/AA (d)                                             3.3
Not Rated (e)                                         Not Rated (e)                                          3.7
                                                                                                            ______
                                                                                                           100.0%
                                                                                                           ======
</TABLE>

NOTES TO STATEMENT OF INVESTMENT:
    (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, 1996, 57.7% 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 Fund's Board of Trustees to be
    of comparable quality to those rated securities in which the Fund may
    invest.
    (f)  At January 31, 1996, the Fund had $145,450,000 (32.5% of net assets)
    invested in securities whose payment of prinicipal and  interest is
    dependent upon revenues generated from housing projects.




See independent accountants' review report and notes to financial statements.

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                              JANUARY 31, 1996 (UNAUDITED)
<S>                                                                                               <C>            <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                     $456,902,081
    Cash....................................................................                                          606,677
    Interest receivable.....................................................                                        3,216,367
    Prepaid expenses........................................................                                            8,888
                                                                                                                   _________
                                                                                                                  460,734,013
LIABILITIES:
    Due to The Dreyfus Corporation and subsidiaries.........................                      $   214,021
    Payable for investment securities purchased.............................                       13,350,000
    Accrued expenses and other liabilities..................................                          134,866      13,698,887
                                                                                                     ________       _________
NET ASSETS  ................................................................                                     $447,035,126
                                                                                                                  ============
REPRESENTED BY:
    Paid-in capital.........................................................                                     $447,190,252
    Accumulated net realized (loss) on investments..........................                                         (155,126)
                                                                                                                   _________
NET ASSETS at value.........................................................                                     $447,035,126
                                                                                                                 ============
Shares of Beneficial Interest outstanding:
    Class A Shares
      (unlimited number of $.001 par value shares authorized)...............                                      447,189,150
                                                                                                                  ===========
    Class B Shares
      (unlimited number of $.001 par value shares authorized)...............                                            1,102
                                                                                                                  ===========
NET ASSET VALUE per share:
    Class A Shares
      ($447,034,024 / 447,189,150)..........................................                                            $1.00
                                                                                                                      =======
    Class B Shares
      ($1,102 / 1,102 shares)...............................................                                            $1.00
                                                                                                                      =======



</TABLE>
See independent accountants' review report and notes to financial statements.

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS                                                         SIX MONTHS ENDED JANUARY 31, 1996 (UNAUDITED)
<S>                                                                                               <C>               <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                        $8,678,581
    EXPENSES:
      Management fee-Note 2(a)..............................................                      $1,170,660
      Shareholder servicing costs-Note 2(c).................................                         164,185
      Professional fees.....................................................                          29,968
      Custodian fees........................................................                          24,152
      Trustees' fees and expenses-Note 2(d).................................                          12,262
      Prospectus and shareholders' reports..................................                           9,703
      Registration fees.....................................................                           9,192
      Miscellaneous.........................................................                          10,033
                                                                                                     _______
          TOTAL EXPENSES....................................................                                         1,430,155
                                                                                                                     _________
INVESTMENT INCOME-NET.......................................................                                         7,248,426
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                            (6,727)
                                                                                                                     _________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                        $7,241,699
                                                                                                                    ==========



See independet accountants' review report and notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                      YEAR ENDED             SIX MONTHS ENDED
                                                                                        JULY 31,              JANUARY 31, 1996
                                                                                         1995                    (UNAUDITED)
                                                                                      ___________                _________
<S>                                                                              <C>                          <C>
OPERATIONS:
    Investment income-net.............................................           $  16,752,063                $  7,248,426
    Net realized (loss) on investments................................                 (28,743)                     (6,727)
                                                                                _______________                 ____________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........              16,723,320                   7,241,699
                                                                                _______________                 ____________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................             (16,752,063)                 (7,248,424)
      Class B shares..................................................                 --                               (2)
                                                                                _______________                 ____________
          TOTAL DIVIDENDS.............................................             (16,752,063)                 (7,248,426)
                                                                                _______________                 ____________
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................           1,802,148,457                 757,311,053
      Class B shares..................................................                 --                            1,100
    Dividends reinvested:
      Class A shares..................................................              15,289,984                   6,583,585
      Class B shares..................................................                 --                                2
      Cost of shares redeemed:
      Class A shares..................................................          (2,053,110,924)               (780,257,640)
                                                                                  ______________              _____________
          (DECREASE) IN NET ASSETS FROM BENEFICIAL
            INTEREST TRANSACTIONS.....................................            (235,672,483)                (16,361,900)
                                                                                   _____________              _____________
            TOTAL (DECREASE) IN NET ASSETS............................            (235,701,226)                (16,368,627)
NET ASSETS:
    Beginning of period...............................................             699,104,979                 463,403,753
                                                                                   _____________              _____________
    End of period.....................................................        $    463,403,753              $  447,035,126
                                                                                   =============             =============


</TABLE>
See independent accountants' review report and notes to financial statements.

<TABLE>
<CAPTION>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.

                                                                  CLASS A SHARES                               CLASS B SHARES
                                   -----------------------------------------------------------------------    ---------------
                                                                                          SIX MONTHS ENDED    SIX MONTHS ENDED
                                                        YEAR ENDED JULY 31,               JANUARY 31, 1996    JANUARY 31, 1996
                                   --------------------------------------------------                            (UNAUDITED)(1)
PER SHARE DATA:                        1991      1992      1993      1994       1995        (UNAUDITED)
                                     ------     ------    ------     -----     ------        ----------            -----------
    <S>                             <C>       <C>       <C>        <C>        <C>            <C>                 <C>
    Net asset value, beginning
      of period..........           $ 1.00    $ 1.00    $ 1.00     $ 1.00     $ 1.00         $ 1.00              $ 1.00
                                     ------     ------    -----      -----     ------          ------              ------
    INVESTMENT OPERATIONS;
   Investment income-net.              .052      .036      .024       .023       .031           .016                .014
                                     ------     ------    -----      -----     ------          ------              ------
    DISTRIBUTIONS;
    Dividends from investment
      income-net.........             (.052)    (.036)    (.024)     (.023)     (.031)         (.016)               (.014)
                                     ------     ------    -----      -----     ------          ------              ------
    Net asset value, end
      of period..........           $ 1.00    $ 1.00    $ 1.00     $ 1.00     $ 1.00         $ 1.00              $ 1.00
                                     ======     =======  ======     ======    =======        ========             =======
TOTAL INVESTMENT
    RETURN  ............              5.29%     3.65%     2.46%      2.27%      3.14%          3.11%(2)           2.72%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average
      net assets........               .02%      .20%      .33%       .33%       .52%           .61%(2)           1.67%(2)
    Ratio of net investment
      income to average
      net assets........              5.08%     3.59%     2.43%      2.24%      3.07%          3.09%(2)           2.95%(2)
    Decrease reflected in above
      expense ratios due to
      undertakings by
      the Manager........              .59%      .41%      .30%       .28%       .11%             --                 .-
    Net asset value,
      end of period
      (000's Omitted)....           $538,978   $549,383  $608,534  $699,105   $463,404         $447,034             $1
    (1)  From August 1, 1995 (commencement of initial offering) to Janaury 31, 1996.
    (2)  Annualized.


See independent accountants' review report and notes to financial statements.
</TABLE>

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    General California Municipal Money Market Fund (the "Fund") is registered
under the Investment Company Act of 1940 ("Act") as a non-diversified
open-end management investment company. The Fund's investment objective is to
maximize current income exempt from Federal and State of California income
taxes to the extent consistent with the preservation of capital and the
maintenance of liquidity. The Dreyfus Corporation ("Manager") serves as the
Fund's investment adviser. The Manager is a direct subsidiary of Mellon Bank,
N.A. Premier Mutual Fund Services, Inc. (the "Distributor") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales charge.
    On July 19, 1995, the Fund's Board of Trustees approved an amendment to
the Fund's Agreement and Declaration of Trust to provide for the issuance of
additional shares of the Fund. The amendment was approved by Fund
shareholders on September 1, 1994. Pursuant to the amendment, the Fund's
existing authorized shares were classified as Class A shares and an unlimited
number of authorized and unissued shares of Beneficial Interest of the Fund,
par value $.001 per share, were classified as Class B shares. The Fund began
offering both Class A and Class B shares on August 1, 1995. Class A shares
and Class B shares are identical except as to the services offered to and the
expenses borne by each class and certain voting rights. Class B shares are
subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act
and, in addition, Class B shares are charged directly for sub-accounting
services provided by service agents at an annual rate of .05% of the value of
the average daily net assets of Class B.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so. There is no
assurance, however, that the Fund will be able to maintain a stable net asset
value of $1.00.
    (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.
    The Fund follows an investment policy of investing primarily in municipal
obligations of one state. Economic changes affecting the state and certain of
its public bodies and municipalities may affect the ability of issuers within
the state to pay interest on, or repay principal of, municipal obligations
held by the Fund.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain, if any, are normally declared and
paid annually, but the Fund may make distributions on a more frequent basis
to comply with the distribution requirements of the Internal Revenue Code. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.

GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
    The Fund has an unused capital loss carryover of approximately $122,000
available for Federal income tax purposes to be
applied against future net securities profits, if any, realized subsequent to
July 31, 1995. The carryover does not include net realized securities losses
from November 1, 1994 through July 31, 1995 which are treated for Federal
income tax purposes, as arising in fiscal 1996. If not applied, $8,200 of the
carryover expires in fiscal 2002 and $113,800 expires in fiscal 2003.
    At January 31, 1996, the cost of investments for Federal income tax
purposes was substantially the same as the cost for financial reporting
purposes (see the Statement of Investments).
NOTE 2-MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the average
daily value of the Fund's net assets and is payable monthly. The Agreement
provides for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed 1 1\2% of the average value of the Fund's net
assets for any full fiscal year. There was no expense reimbursement for the
six months ended January 31, 1996.
    Effective December 1, 1995, the Fund compensates Dreyfus Transfer, Inc.,
a wholly-owned subsidiary of the Manager, under a transfer agency agreement
for providing personnel and facilities to perform transfer agency services
for the Fund. Such compensation amounted to $19,602 for the period from
December 1, 1995 through January 31, 1996.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, effective
August 1, 1995 the Fund directly bears the cost of preparing, printing and
distributing prospectuses and statements of additional information and of
implementing and operating the Class B Distribution Plan. In addition, the
Fund reimburses the Distributor for payments made to third parties for
distributing the Fund's Class B shares at an aggregate annual rate of up to
 .20% of the value of the average daily net assets of Class B. During the six
months ended January 31, 1996, there was no amount charged to the Fund
pursuant to the Class B Distribution Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, with respect to
Class A ("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus
Service Corporation, a wholly-owned subsidiary of the Manager, an amount not
to exceed an annual rate of .25 of 1% of the value of the Fund's average
daily net of assets of Class A for certain allocated expenses of providing
personal services and/or maintaining shareholder accounts. The services
provided may include personal services relating to shareholder accounts, such
as answering shareholder inquiries regarding the Fund and providing reports
and other information, and services related to the maintenance of shareholder
accounts. During the six months ended January 31, 1996, the Fund was charged
an aggregate of $95,435 pursuant to the Class A Shareholder Services Plan.
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), effective August 1, 1995, the Fund pays the
Distributor, at an annual rate of .25 of 1% of the value of the average daily
net assets of Class B shares for servicing shareholder accounts. The services
provided may include personal services relating to shareholder accounts, such
as answering shareholder inquiries regarding the Fund and providing reports
and other information, and services related to the
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
maintenance of shareholder accounts. The Distributor may make payments to
Service Agents in respect of their services. The Distributor determines the
amounts to be paid to Service Agents.
    The Manager has currently undertaken through July 31, 1996, that if the
aggregate expenses of Class B of the Fund, (excluding certain expenses as
described above) exceed 1% 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 relating to Class B to the extent of any excess expense and up
to the full fee payable under such Plan. During the six months ended January
31, 1996, there was no amount charged to the Fund pursuant to the Class B
Shareholder Services Plan.
    (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
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
    We have reviewed the accompanying statement of assets and liabilities of
General California Municipal Money Market Fund, including the statement of
investments, as of January 31, 1996, and the related statements of operations
and changes in net assets and financial highlights for the six month period
ended January 31, 1996. These financial statements and financial highlights
are the responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
July 31, 1995 and financial highlights for each of the two years in the
period ended July 31, 1995 and in our report dated September 1, 1995, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.
                              [Ernst & Young signature logo]

New York, New York
March 7, 1996

[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.
One American Express Plaza
Providence, RI 02903




Further information is contained
in the Prospectus, which must
precede or accompany this report.




Printed in U.S.A.                        573/699SA961
[Dreyfus logo]
General California
Municipal
Money Market Fund
Semi-Annual
Report
January 31, 1996



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