GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
N-30D, 1999-08-06
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General California
Municipal Money
Market Fund

SEMIANNUAL REPORT
May 31, 1999


<PAGE>

The views expressed herein are current to the date of this report. These views
and the composition of the fund's portfolio are subject to change at any time
based on market and other conditions.

  * Not FDIC-Insured
  * Not Bank-Guaranteed
  * May Lose Value


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.


<PAGE>

                                    Contents

                                    THE FUND
- --------------------------------------------

                              2     Letter from the President

                              3     Discussion of Fund Performance

                              6     Statement of Investments

                             11     Statement of Assets and Liabilities

                             12     Statement of Operations

                             13     Statement of Changes in Net Assets

                             14     Financial Highlights

                             16     Notes to Financial Statements

                                    FOR MORE INFORMATION
- --------------------------------------------------------

                                    Back Cover


<PAGE>

                                                  General California    The Fund
                                         Municipal Money Market Fund


LETTER FROM THE PRESIDENT
- -------------------------
Dear Shareholder:

We are pleased to present this semiannual report for General California
Municipal Money Market Fund, covering the six-month period from December 1, 1998
through May 31, 1999. Inside, you'll find valuable information about how the
fund was managed during the reporting period, including a discussion with the
fund's portfolio manager, Jill Shaffro.

Yields on both taxable and tax-exempt money market securities generally declined
early in the reporting period in the wake of the Federal Reserve Board's
decision in the fall of 1998 to ease monetary policy. While the U.S. economy has
continued to grow, the Federal Reserve was concerned about persistent economic
weakness abroad. Their adoption of lower short-term interest rates was intended
to stimulate not just domestic economic growth, but the economies of other
nations as well.

Despite lower nominal interest rates for tax-exempt money market instruments,
very low inflation continued to support attractive real returns, which are
nominal yields less the rate of inflation.

We appreciate your confidence over the past six months, and we look forward to
your continued participation in General California Municipal Money Market Fund.

Sincerely,

/s/ Stephen E. Canter

Stephen E. Canter
President and Chief Investment Officer
The Dreyfus Corporation
June 14, 1999


2


<PAGE>

DISCUSSION OF FUND PERFORMANCE
- ------------------------------
Jill Shaffro, Portfolio Manager

How did General California Municipal Money Market Fund perform during the
period?

For the six-month period ended May 31, 1999, General California Municipal Money
Market Fund produced a tax-exempt yield of 2.38% for Class A shares and 1.99%
for Class B shares. After taking into account the effect of compounding, the
fund's Class A shares provided an annualized effective yield of 2.41% while the
fund's Class B shares produced an annualized effective yield of 2.01%(1)

For the six-month period ended May 31, 1999, the fund's Class A shares and Class
B shares produced total returns of 1.19% and 1.00%,(2) respectively, compared to
the Lipper California Tax-Exempt Money Market Funds category average total
return of 1.18% for the same time period. (3)

What is the fund's investment approach?

Our goal is to seek a high level of federal and California tax-exempt income
while maintaining a stable $1.00 share price. We also seek to provide a
competitive total return, and we attempt to be especially vigilant in our
efforts to preserve capital.

To achieve these objectives, we employ two primary strategies. First, we attempt
to add value by constructing a diverse portfolio of high-quality, tax-exempt
money market instruments from California-exempt issuers. Second, we actively
manage the portfolio's average maturity in anticipation of interest rate trends
and supply-and-demand changes in California's short-term municipal marketplace.

For example, if we expect supply to increase temporarily when many
municipalities issue short-term debt at once -- as they tend to in June and
July, for example -- we may reduce the portfolio's average maturity to make
cash available for the purchase of higher yielding securities.  That's because
yields tend to rise if many issuers are competing for

                                                            The Fund  3
<PAGE>

DISCUSSION OF FUND PERFORMANCE (continued)


investor interest. If we expect demand to surge at a time when we anticipate
little issuance and, therefore, lower yields -- as often happens in
January -- we may increase the portfolio's average maturity to maintain
current yields for as long as practical. At other times, we try to maintain
an average maturity that reflects our view of short-term interest rate trends.

What other factors influenced the fund's performance?

Although the fund, by definition, primarily contains securities from California
issuers, the entire U.S. fixed-income marketplace was influenced during the
reporting period by economic events overseas. When the Asian currency and credit
crisis threatened Latin America last summer and fall, the Federal Reserve Board
and other central banks reduced key short-term interest rates. This move was
intended to help boost economic activity by making borrowing less expensive for
corporations. An additional consequence was lower yields on money market
securities.

Despite economic weakness in some overseas markets, the U.S. and California
economies remained strong. Because municipalities have enjoyed higher tax
revenues during this period of economic prosperity, many have had less need to
borrow. As a result, fewer tax-exempt money market securities were issued in
California than in the same 12-month period one year ago. Yet, demand from
investors seeking to minimize their income tax liabilities remained high.
This imbalance helped push short-term tax-exempt yields down further during
the second half of 1998.  Tax-exempt yields have remained relatively stable
so far in 1999.

4


<PAGE>

What is the fund's current strategy?

We have continued to focus on high-quality money market instruments from a wide
array of California issuers. Some of the most frequently used instruments
include Variable Rate Demand Notes (VRDNs), which are issued by investment banks
through the securitization of longer-term municipal bonds. With a put feature of
either one or seven days attached to each VRDN, we believe that VRDNs afford a
high degree of liquidity as well as high quality to the portfolio. Accordingly,
as of May 31, 1999, more than half of the portfolio was composed of VRDNs. The
remainder was comprised of tax-exempt commercial paper as well as municipal
notes issued by California and by Puerto Rico, whose municipal bonds provide
income exempt from federal and state income taxes for virtually all U.S.
residents.

June 14, 1999

[FN]
1 Annualized effective yield is based upon dividends declared daily and
  reinvested monthly. Past performance is no guarantee of future results. Yields
  fluctuate. An investment in the fund is not insured or guaranteed by the FDIC
  or any other government agency. Although the fund seeks to preserve the value
  of your investment at $1.00 per share, it is possible to lose money by
  investing in the fund.

2 Total return includes reinvestment of dividends. The fund's Class B shares'
  return figure provided reflects the absorption of fund expenses by The Dreyfus
  Corporation pursuant to an undertaking in effect that may be extended,
  terminated or modified at any time. Had these expenses not been absorbed, the
  fund's Class B shares' return would have been lower. Income may be subject to
  state and local taxes for non-California residents, and some income may be
  subject to the Federal Alternative Minimum Tax (AMT) for certain shareholders.

3 Source: Lipper Analytical Services, Inc.
</FN>

                                                                     The Fund  5


<PAGE>

STATEMENT OF INVESTMENTS

May 31, 1999 (Unaudited)

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                             Principal
Tax Exempt Investments--98.7%                                Amount ($)            Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                         <C>                  <C>
California--89.2%

Alameda County, TRAN 4.50%, 7/7/1999                         5,000,000            5,004,282

Alameda County Industrial Development Authority,
   Revenue, VRDN
   (Spectrum Label Corp.)
   3.35%, 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 Economic Development Finance Authority,
   Revenue, VRDN:
     (California Independent System Project):
       3.20% (LOC; Bank of America)(a)                       5,300,000            5,300,000
       3.25% (LOC; Bank of America)(a)                       5,200,000            5,200,000
     Refunding
       (Kqed Inc. Project)
       3.10% (LOC; Wells Fargo Bank)(a)                      4,000,000            4,000,000

California Health Facilities Financing Authority,
   Revenue, VRDN
   (Catholic Health Care)
   2.90%, Series D (Insured; MBIA and Liquidity
   Facility; Rabobank Nederland)(a)                         10,400,000           10,400,000

California Housing Finance Agency,
   Single Family Mortgage Purchase Revenue
   3%, Series B, 7/1/2000                                   6,870,000             6,870,000

California Pollution Control Financing Authority VRDN:
   PCR:
     (Southern California Edison)
       3.45%, Series A (Corp. Guaranty; Southern
       California Edison Co.)(a)                             5,000,000            5,000,000
     Refunding (Pacific Gas and Electric):
       3%, Series A (LOC; Union Bank of Switzerland)(a)      5,000,000            5,000,000
       3.05%, Series B (LOC; Rabobank Nederland)(a)          6,400,000            6,400,000
       3.30%, Series A (LOC; Toronto-Dominion Bank)(a)       5,000,000            5,000,000
       3.30%, Series C (LOC; Bank of America)(a)             7,000,000            7,000,000
       3.40%, Series E (LOC; Morgan Guaranty
         Trust Co.)(a)                                      13,000,000           13,000,000
   RRR, Refunding (Ultra Power Rocklin Project)
     3.30%, Series A (LOC; Bank of America)(a)               7,600,000            7,600,000
   SWDR:
     (Colmac Energy Project) 3.05%, Series A
       (LOC; Union Bank of Switzerland)(a)                   6,500,000            6,500,000
     (Shell Martinez Refining) 3.20%, Series A
       (Corp Guaranty; Shell Oil Co.)(a)                     6,800,000            6,800,000
</TABLE>

6


<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                             Principal
Tax Exempt Investments (continued)                           Amount ($)            Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                         <C>                  <C>
California (continued)

California Pollution Control Financing
   Authority VRDN (continued):
   SWDR (continued):
     (Shell Oil Martinez Project) 3.30%, Series B
       (Corp Guaranty; Shell Oil Co.)(a)                     1,900,000           1, 900,000

California Public Capital Improvements Financing
   Authority, Revenue
   (Pooled Project) 2.95%, Series C, 6/15/1999
   (LOC; National Westminister Bank)                        14,000,000           14,000,000

California School Cash Reserve Program Authority,
   4.50%, Series A, 7/2/1999 (Insured; AMBAC)               10,000,000           10,006,217

California School Facilities Financing Corporation,
   COP, VRDN (Capital Improvements Financing Project)
   3.60%, Series D (LOC; Kredietbank)(a)                    10,000,000           10,000,000

State of California:
   3.20%, Series BJ, 6/1/1999                               15,000,000           15,001,170
   4.125%, Series BJ, 6/1/1999                                 975,000              975,000
   CP 3.10%, 7/7/1999 (LOC: Bank of Novia Scotia,
     Bayerische Landesbank, Commerz Bank,
     Credit Agricole De France, Credit Local De France,
     Landesbank Hessen, Morgan Guaranty Trust Co.,
     State Street Bank, Toronto-Dominion Bank, and
     Westdeutsche Landesbank)(a)                            15,000,000           15,000,000
   RAN 4%, 6/30/1999                                        13,000,000           13,007,320

California Statewide Community Development
   Authority, Multi-Family Revenue, VRDN
   (Canyon Creek Apartments)
   3.15%, 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)                 6,500,000            6,500,000

City of Clovis MFHR, VRDN
   (Fowler Place Apartments Project)
   3.25% (LOC; Wells Fargo Bank)(a)                          7,200,000            7,200,000

City of Clovis Unified School District, COP,
   Capital Project, VRDN
   (Flower Place Apartments Project)
   3.40% (LOC; Wells Fargo Bank)(a)                            100,000              100,000

Dublin, MFHR, Authority, VRDN (Park Sierra)
   3.10%, Series A (LOC; Kredietbank)(a)                     4,400,000            4,400,000

Fresno, MFHR, Refunding, VRDN
   (Heron Points Apartments)
   3.10% (LOC; Wells Fargo Bank)(a)                          5,000,000            5,000,000
</TABLE>

                                                                     The Fund  7


<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)
<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                             Principal
Tax Exempt Investments (continued)                           Amount ($)            Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                         <C>                  <C>
California (continued)
Huntington Beach, MFHR, VRDN
   (Five Points Seniors Project)
   3.55%, Series A (Corp. Guaranty; FNMA)(a)                 3,100,000            3,100,000

Irwindale, IDR, VRDN (Toys "R" Us Inc. Project)
   3.475% (LOC; Bankers Trust Co.)(a)                        3,000,000            3,000,000

Kern County Board of Education, TRAN
   4.25%, 6/30/1999                                          9,000,000            9,004,465

Los Angeles, VRDN:
   MFHR
     (Beverly Park Apartments) 3.35%, Series A
     (LOC; Federal Home Loan Banks)(a)                       9,600,000            9,600,000
   Multi-Family Revenue (Loans To Lender Program)
     3.30%, Series B (LOC; Federal Home Loan Banks)(a)      10,000,000           10,000,000

Los Angeles County Metropolitan Transportation
   Authority, Sales Tax Revenue, Refunding, VRDN
   2.90%, Series A (Insured; MBIA and Liquidity
   Facility; Credit Locale de France)(a)                    11,000,000           11,000,000

Los Angeles County Transport Commission,
   Sales Tax Revenue, Refunding, VRDN
   2.95%, Series A (LOC; Bayerische Landesbank and
   Insured; FGIC)(a)                                        11,400,000           11,400,000

Newport Beach, Revenue, VRDN:
   3.25%, Series A (Hoag Member Hospital)(a)                 7,800,000            7,800,000
   3.25%, (Hoag Member Hospital Presbyterian)(a)            27,860,000           27,860,000

Oakland Joint Powers Financing Authority,
   Lease Revenue, 3%, Series A-2
   (LOC; Commerzbank and Insured; FSA)(a)                    5,000,000            5,000,000

Orange County, Apartment Development Revenue, VRDN:
   (Foothill Oaks Apartment) 3.15%, Series B
     (LOC; Bank of America)(a)                               5,000,000            5,000,000
   Refunding:
     (Villa La Paz) 2.95%, Series F (LOC; FNMA)(a)          11,500,000           11,500,000
     (Wlco LF) 2.95%, Series G, (LOC; FNMA)(a)               5,000,000            5,000,000

San Bernardino County, Refunding, VRDN:
   COP (Medical Center Financing Project)
     3%, (LOC; Landesbank Hessen and Insured; MBIA)(a)       9,500,000            9,500,000
   MFHR:
     (Evergreen Apartments) 2.95%, Series A
       (LOC; FNMA)(a)                                        4,700,000            4,700,000
     (Sycamore Terrace) 2.95%, Series A (LOC; FNMA)(a)       2,850,000            2,850,000

San Francisco Bay Area Rapid Transit District, CP
   3.15%, Series B, 7/7/1999
   (LOC; Union Bank of Switzerland)                          8,500,000            8,500,000
</TABLE>

8


<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                             Principal
Tax Exempt Investments (continued)                           Amount ($)            Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                         <C>                  <C>
California (continued)

San Jose, MFHR, VRDN
   (Sienna at Renaissance Square Apartments)
   3.20%, Series A (LOC; Key Bank Inc.)(a)                  12,000,000           12,000,000

Santa Cruz County Board of Education, TRAN
   3.45%, 6/30/1999                                          5,000,000            5,001,223

Simi Valley, MFHR, VRDN (Shadowridge Apartments)
   3.10% (LOC; Citibank)(a)                                  7,900,000            7,900,000

University of California, Board of Regents, Revenues, CP
   2.75%, 7/22/1999 (LOC; Bank of America,
   Bank of Montreal, Canadian Imperial Bank of
   Commerce, Credit Agricole and Societe Generale)           6,000,000            6,000,000

U.S. Related--9.5%

Commonwealth of Puerto Rico:
   Government Development Bank, CP:
     2.80%, 7/7/1999                                         2,333,000            2,333,000
     2.75%, 7/22/1999                                        7,516,000            7,516,000
     3%, 8/9/1999                                            8,000,000            8,000,000
   TRAN 3.50%, Series A, 7/30/99                            18,000,000          18,019, 432

Commonwealth of Puerto Rico Highway and
   Transportation Authority,
   Transportation Revenue, VRDN
   3%, Series A (LOC; Bank of Nova Scotia and
   Insured; AMBAC)(a)                                        3,000,000            3,000,000

Puerto Rico Industrial Tourist Education, Medical and
   Environmental Control Facilities,
   Financing Authority Higher Education, Revenues, VRDN
   (Ana G. Mendez University System Project)
   3.05%, Series A (LOC; Banco Popular)(a)                   4,000,000            4,000,000
- --------------------------------------------------------------------------------------------

Total Investments (cost $445,398,109)                            98.7%          445,398,109

Cash and Receivables (Net)                                        1.3%            6,046,001

Net Assets                                                      100.0%          451,444,110
</TABLE>

                                                                     The Fund  9

<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
Summary of Abbreviations

<S>       <C>                                    <C>      <C>
AMBAC     American Municipal Bond                MBIA     Municipal Bond Investors
            Assurance Corporation                           Assurance 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
LOC       Letter of Credit                                  Notes
                                                 VRDN     Variable Rate Demand Notes
</TABLE>


- -------------------------------------------------------------------------------
Summary of Combined Ratings

Fitch             or      Moody's     or  Standard & Poor's        Value (%)
- -------------------------------------------------------------------------------
F1+/F1                    VMIG1/MIG1, P1  SP1+/SP1, A1+/A1                 97.1
AAA/AA(b)                 Aaa/Aa(b)       AAA/AA(b)                         2.3
Not Rated(c)              Not Rated(c)    Not Rated(c)                       .6
                                                                          100.0

[FN]
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 May 31, 1999 the fund had $122,370,000 (36.9%) invested in securities whose
  payment of principal and interest is dependent upon revenues generated from
  housing projects.

See notes to financial statements.
</FN>
10


<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
May 31, 1999 (Unaudited)

<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------
                                                                            Cost          Value
- ------------------------------------------------------------------------------------------------
<S>                                                                  <C>            <C>
Assets ($):
Investments in securities--See Statement of Investments              445,398,109    445,398,109
Cash                                                                                  2,681,364
Interest receivable                                                                   3,571,514
Prepaid expenses and other assets                                                        51,042
                                                                                    451,702,029
- ------------------------------------------------------------------------------------------------
Liabilities ($):
Due to The Dreyfus Corporation and affiliates                                           191,599
Accrued expenses                                                                         66,320
                                                                                        257,919
- ------------------------------------------------------------------------------------------------
Net Assets ($)                                                                      451,444,110
- ------------------------------------------------------------------------------------------------
Composition of Net Assets ($):
Paid-in capital                                                                     451,644,176
Accumulated net realized gain (loss) on investments                                    (200,066)
- ------------------------------------------------------------------------------------------------
Net Assets ($)                                                                      451,444,110


<CAPTION>
- ------------------------------------------------------------------------------------------------
Net Asset Value Per Share
                                                                         Class A        Class B
- ------------------------------------------------------------------------------------------------
<S>                                                                  <C>            <C>
Net Assets ($)                                                       404,431,877     47,012,233
Shares Outstanding                                                   404,631,995     47,012,181
- ------------------------------------------------------------------------------------------------
Net Asset Value Per Share ($)                                               1.00           1.00
</TABLE>


See notes to financial statements.


                                                                    The Fund  11


<PAGE>

STATEMENT OF OPERATIONS
Six Months Ended May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------
Investment Income ($)
- --------------------------------------------------------------------------------
Interest Income                                                       5,980,130
Expenses:
Management fee--Note 2(a)                                               994,453
Shareholder servicing costs--Note 2(c)                                  160,042
Registration fees                                                        33,124
Professional fees                                                        23,792
Custodian fees                                                           21,557
Prospectus and shareholders' reports                                     15,865
Trustees' fees and expenses--Note 2(d)                                   13,574
Distribution fees (Class B)--Note 2(b)                                   10,729
Miscellaneous                                                             4,683
Total Expenses                                                        1,277,819
Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                                (14,173)
Net Expenses                                                          1,263,646
Investment Income--Net                                                4,716,484
- --------------------------------------------------------------------------------
Net Realized Gain (Loss) on Investments--Note 1(b)($)                     3,557
Net Increase in Net Assets Resulting from Operations                  4,720,041



See notes to financial statements.

12


<PAGE>

STATEMENT OF CHANGES IN NET ASSETS

<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------
                                                           Six Months Ended
                                                               May 31, 1999          Year Ended
                                                                 (Unaudited)  November 30, 1998
- ------------------------------------------------------------------------------------------------
<S>                                                               <C>                 <C>
Operations ($):
Investment income--net                                            4,716,484           9,790,386
Net realized gain (loss) on investments                               3,557              (8,381)
Net Increase (Decrease) in Net Assets
  Resulting from Operations                                       4,720,041           9,782,005
- ------------------------------------------------------------------------------------------------
Dividends to Shareholders from ($):
Investment income--net:
Class A shares                                                   (4,607,404)         (9,626,016)
Class B shares                                                     (109,080)           (164,370)
Total Dividends                                                  (4,716,484)         (9,790,386)
- ------------------------------------------------------------------------------------------------
Beneficial Interest Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A shares                                                  693,882,023         820,634,796
Class B shares                                                   59,727,476          57,212,398
Dividends reinvested:
Class A shares                                                    4,225,473           8,929,793
Class B shares                                                      108,575             162,222
Cost of shares redeemed:
Class A shares                                                 (629,405,006)       (854,932,309)
Class B shares                                                  (21,583,744)        (51,283,460)
Increase (Decrease) in Net Assets from
  Beneficial Interest Transactions                              106,954,797         (19,276,560)
Total Increase (Decrease) in Net Assets                         106,958,354         (19,284,941)
- ------------------------------------------------------------------------------------------------
Net Assets ($):
Beginning of Period                                             344,485,756         363,770,697
End of Period                                                   451,444,110         344,485,756
</TABLE>

See notes to financial statements.

                                                                    The Fund  13


<PAGE>

FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the
fiscal periods indicated. Certain information reflects financial results for a
single fund share. Total return shows how much your investment in the fund would
have increased (or decreased) during each period, assuming you had reinvested
all dividends and distributions. These figures have been derived from the fund's
financial statements.

<TABLE>
<CAPTION>
- -----------------------------------------------------------------------------------------------------
                             Six Months                 Four Months
                                  Ended    Year Ended         Ended          Year Ended July 31,
                           May 31, 1999  November 30,  November 30,    -----------------------------
Class A Shares               (Unaudited)         1998          1997(a)  1997    1996    1995    1994
- -----------------------------------------------------------------------------------------------------
<S>                             <C>           <C>           <C>      <C>     <C>     <C>     <C>
Per Share Data ($):
Net asset value, beginning
  of period                        1.00          1.00          1.00     1.00    1.00    1.00    1.00
Investment Operations:
Investment income--net             .011          .027          .010     .029    .029    .031    .023
Distributions:
Dividends from investment
  income--net                     (.011)        (.027)        (.010)   (.029)  (.029)  (.031)  (.023)
Net asset value, end of period     1.00          1.00          1.00     1.00    1.00    1.00    1.00
- -----------------------------------------------------------------------------------------------------
Total Return (%)                   2.39(b)       2.78          2.96(b)  2.95    2.94    3.14    2.27
- -----------------------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average
  net assets                        .63(b)        .64           .70(b)   .64     .65     .52     .33
Ratio of net investment income
  to average net assets            2.38(b)       2.74          2.97(b)  2.91    2.91    3.07    2.24
Decrease reflected in above
  expense ratios due to
  undertakings by the Manager        --            --            --       --      --     .11     .28
Net Assets, end of period
  ($ x 1,000)                   404,432       335,726       361,102  327,226 390,155 463,404 699,105

<FN>
a The fund changed its fiscal year end from July 31 to November 30.
b Annualized.
</FN>
</TABLE>

See notes to financial statements.

14


<PAGE>

<TABLE>
<CAPTION>
- -------------------------------------------------------------------------------------------------------
                                      Six Months                 Four Months
                                           Ended    Year Ended         Ended       Year Ended July 31,
                                    May 31, 1999  November 30,  November 30,     ----------------------
Class B Shares                        (Unaudited)         1998          1997(a)    1997         1996(b)
- -------------------------------------------------------------------------------------------------------
<S>                                       <C>            <C>           <C>        <C>          <C>
Per Share Data ($):
Net asset value, beginning of period        1.00          1.00          1.00       1.00         1.00
Investment Operations:
Investment income--net                      .002          .024          .009       .026         .025
Distributions:
Dividends from investment income--net      (.002)        (.024)        (.009)     (.026)       (.025)
Net asset value, end of period              1.00          1.00          1.00       1.00         1.00
- -------------------------------------------------------------------------------------------------------
Total Return (%):                           2.01(c)       2.39          2.57(c)    2.61         2.56
- -------------------------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average net assets     1.00(c)       1.00          1.00(c)    1.00         1.00
Ratio of net investment income
  to average net assets                     2.03(c)       2.34          2.62(c)    2.52         2.45
Decrease reflected in above expense ratios
  due to undertakings by the Manager         .26(c)        .07           .13(c)     .07          .08
Net Assets, end of period ($ x 1,000)     47,012         8,760         2,669        928        5,475

<FN>
a The fund changed its fiscal year end from July 31 to November 30.
b From August 1, 1995 (commencement of initial offering) to July 31, 1996.
c Annualized.
</FN>
</TABLE>

See notes to financial statements.
                                                                    The Fund  15


<PAGE>

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, 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") is the distributor of the
fund's shares, which are sold to the public without a sales load. The fund is
authorized to issue an unlimited number of $.001 par value shares in the
following classes of shares: Class A and Class B. Class A shares and Class B
shares are identical except for the services offered to and the expenses borne
by each class and certain voting rights. Class B shares are subject to a
Distribution Plan adopted pursuant to Rule 12b-1 under the Act and, in addition,
Class B shares are charged directly for sub-accounting services provided by
Service Agents (a securities dealer, financial institution or other industry
professional) at an annual rate of .05% of the value of the average daily net
assets of Class B shares.

It is the fund's policy to maintain a continuous net asset value per share of
$1.00; the fund has adopted certain investment, portfolio valuation and dividend
and distribution policies to enable it to do so. There is no assurance, however,
that the fund will be able to maintain a stable net asset value per share of
$1.00.

The fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

(a) Portfolio valuation: Investments in securities are valued at amortized cost,
which has been determined by the fund's Board of Trustees to represent the fair
value of the fund's investments.

16


<PAGE>

(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 $12,874 during the period ended May 31, 1999
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 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

                                                                    The Fund  17


<PAGE>

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

November 30, 1998. If not applied, $8,200 of the carryover expires in fiscal
2001, $113,800 expires in fiscal 2002, $33,000 expires in fiscal 2003, $19,000
expires in fiscal 2004, $21,000 expires in fiscal 2005 and $9,000 expires in
fiscal 2006.

At May 31, 1999, the cost of investments for Federal income tax purposes was
substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

NOTE 2--Management Fee and Other Transactions
With Affiliates:

(a) Pursuant to a management agreement ("Agreement") with the Manager, the
management fee is computed at the annual rate of .50 of 1% of the value of the
fund's average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses, exclusive of taxes,
brokerage, interest on borrowings and extraordinary expenses, exceed 1-1/2% of
the value of the fund's average net assets, the fund may deduct from payments to
be made to the Manager, or the Manager will bear such excess expense. During the
period ended May 31, 1999, there was no expense reimbursement pursuant to the
Agreement.

(b) Under the Distribution Plan with respect to Class B ("Class B Distribution
Plan"), adopted pursuant to Rule 12b-1 under the Act, Class B shares directly
bear the cost of preparing, printing and distributing prospectuses and
statements of additional information and of implementing and operating the Class
B Distribution Plan. In addition, Class B shares reimburse the Distributor for
payments made to third parties for distributing their shares at an annual rate
up to .20 of 1% of the value of the average daily net assets of Class B. During
the period ended May 31, 1999, Class B shares were charged $10,729 pursuant to
the Distribution Plan.

18


<PAGE>

(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 May 31, 1999, Class A shares were charged $84,992 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 May 31, 1999, 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 May 31, 1999, Class B
shares were charged $16,094, of which $14,173 was reimbursed by the Manager.


                                                                    The Fund  19


<PAGE>

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. During the period
ended May 31, 1999, the fund was charged $36,195 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.

20


<PAGE>

For More Information


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

Distributor

Premier Mutual Fund Services, Inc.
60 State Street
Boston, MA 02109



To obtain information:

By telephone
Call 1-800-645-6561

By mail  Write to:
The Dreyfus Family of Funds
144 Glenn Curtiss Boulevard
Uniondale, NY 11556-0144

By E-mail  Send your request
to [email protected]

On the Internet  Information
can be viewed online or
downloaded from:
http://www.dreyfus.com



(C) 1999, Dreyfus Service Corporation        573/699SA995



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