GENERAL MUNICIPAL MONEY MARKET FUND INC
N-30D, 1995-07-28
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this semi-annual report for the
General Municipal Money Market Fund, Inc. For the six-month period ended May
31, 1995, the annualized yield provided by your Fund's Class A shares was
3.45%. Your Fund's Class B shares provided an annualized yield of 3.39% for
the period since inception through May 31, 1995. After taking into account
the effect of compounding, the annualized effective yields were 3.51% and
3.44% respectively.*  Dividends of approximately $.017 in the case of Class A
shares and approximately $.006 in the case of Class B shares paid during the
period were exempt from Federal income tax.**
    Since our last letter, the Federal Reserve Board limited its actions to
just one interest rate hike of 50 basis points which represented a decrease
in magnitude from previous actions. The fact that the increase was smaller
reflected, in part, the belief that some slowing in the economy had occurred.
However, as some economic indicators continued to conflict with that belief,
the argument for at least a moderate hike appeared reasonable at the time.
More recent events suggest the Fed may ease interest rates soon and, in large
part, market levels now reflect those expectations.
    While market fundamentals do affect the short-term municipal market, the
overriding influence continues to be market technical factors (i.e.
supply/demand). Since the rates on those securities in the portfolio which
provide the highest degree of liquidity (1-day and 7-day demand notes) are
adjusted on a daily or weekly basis, your Fund's yield reflects these rapid
adjustments and fluctuates accordingly. As of May 31, rates on such
securities provided an attractive return, trading at better than 75% of the
taxable overnight repurchase rates. We anticipate that these yields will drop
significantly in the coming weeks as many holdings in municipal money market
funds mature at the end of June. However, if previous summer technical
patterns are repeated, we expect the situation should reverse in late July
and August as issuers return to the market with their summer financings.
    In the wake of the Orange County, California bankruptcy filing in
December, we continue to devote our resources to locating those credits which
achieve our high internal standards and which provide your Fund with
attractive returns.  We have included a current Statement of Investments and
recent financial statements for your review and look forward to serving your
investment needs in the future.
                               Very truly yours,

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
June 16, 1995
New York, N.Y.
*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
**Some income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.

<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                                 MAY 31, 1995 (UNAUDITED)

                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                           AMOUNT            VALUE
                                                                                                --------------      --------------
<S>                                                                                             <C>                 <C>
ALASKA-1.9%
City of Valdez, Marine Terminal Revenue, Refunding, VRDN (Exxon Pipeline Co.
Project)
    4.15%, Series A (Corp. Guaranty; Exxon Corp.) (a).......................                    $   5,000,000       $   5,000,000
ARIZONA-5%
Arizona Educational Loan Marketing Corp., Educational Loan Revenue, VRDN
    4.10%, Series A (Insured; MBIA) (a).....................................                        6,500,000           6,500,000
Glendale Industrial Development Authority, HR, VRDN
    (West Valley Camelback) 4% (LOC; Northwest Corp.) (a,b).................                        6,600,000           6,600,000
CALIFORNIA-4.2%
California Housing Finance Agency, Home Mortgage Revenue
    4.30%, Series F-3, 10/2/95 (LOC; Goldman, Sachs & Co.) (b)..............                        3,000,000           3,000,000
California School Cash Reserve Program Authority, Notes 4.50%, 7/5/95.......                        8,000,000           8,005,380
COLORADO-4.5%
Arapohoe County Capital Improvement Trust Fund, Highway Revenue (E-470
Project) 4.45%, Series L, 8/31/95 (LOC; Swiss Bank Corp.) (b)...............                        6,000,000           6,000,000
Denver Urban Renewal Authority, Tax Increment Revenue (Downtown Denver Renewal)
    4.75%, Series A, 8/24/95 (Collateralized In; U.S. Treasury Bills).......                        5,700,000           5,700,000
DELAWARE-.6%
Delaware Economic Development Authority, IDR, VRDN (Orient Chemical Corp.
Project) 4.40% (LOC; Sumitomo Bank) (a,b)...................................                        1,480,000           1,480,000
FLORIDA-6.6%
Pinellas County Health Facilities Authority, Revenue, Refunding, VRDN
    (Pooled Hospital Loan Program) 4.40% (LOC; Chemical Bank) (a,b).........                        8,100,000           8,100,000
Saint Lucie County, PCR, Refunding, VRDN (Florida Power and Light Co.
Project) 4.30% (Corp. Guaranty; Florida Power and Light Co.) (a)............                        9,100,000           9,100,000
HAWAII-3.4%
Honolulu City and County, MFHR, VRDN (Halekua Gardens Project)
    4.35%, Series A (LOC; Bank of Tokyo) (a,b)..............................                        8,873,000           8,873,000
ILLINOIS-10.3%
City of Chicago, Gas Supply Revenue (People's Gas Light and Coke Co.)
    4.95%, Series B, 12/1/95................................................                        9,000,000           9,000,000
Illinois Health Facilities Authority, Revenue, VRDN
    (Resurrection Health Care Systems) 4.55% (LOC: Comerica Bank,
    First Chicago Bank, Lasalle National Bank and National Bank of Detroit) (a,b)                  11,900,000          11,900,000
City of West Chicago, IDR, VRDN (Acme Printing Ink Project)
    4.275% (LOC; Bank of Tokyo) (a,b).......................................                        6,000,000           6,000,000
IOWA-4.3%
Iowa Finance Authority, SWDR, VRDN (Cedar River Paper Co. Project)
    4.45% (LOC; Swiss Bank Corp.) (a,b).....................................                       11,100,000          11,100,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                     MAY 31, 1995 (UNAUDITED)

                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT              VALUE
                                                                                                --------------      --------------
KENTUCKY-1.4%

Boone County, IDR, VRDN (Curtin Matherson Scientific)
    4.85% (LOC; Barclays Bank) (a,b)........................................                    $   2,500,000       $   2,500,000
City of Georgetown, Public Project Revenue, VRDN 4.70% (LOC; Bank of Tokyo) (a,b)                   1,120,000           1,120,000
LOUISIANA-7.9%
East Baton Rouge Parish, PCR, Refunding, VRDN (Exxon Project)
    4.25% (Corp. Guaranty; Exxon Corp.) (a).................................                       10,000,000          10,000,000
Jefferson Parish Hospital Service District Number 2, HR, VRDN
    4.10% (Insured; FGIC) (a)...............................................                        6,000,000           6,000,000
West Baton Rouge Parish Industrial District Number 3, Revenue, VRDN
    (Dow Chemical Co. Project) 4.50% (Corp. Guaranty; Dow Chemical Co.) (a).                        4,500,000           4,500,000
MICHIGAN-5.2%
Macomb Township Economic Development Corp., LOR, VRDN (ACR Industries
Project)
    4.15% (LOC; Comerica Bank) (a,b)........................................                          800,000             800,000
State of Michigan, GO Notes 5%, 9/29/95.....................................                        9,000,000           9,025,843
Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)
    4.30% (LOC; Barclays Bank) (a,b)........................................                        3,800,000           3,800,000
MINNESOTA-2.7%
Minnesota Housing Finance Agency, Single Family Mortgage
    5.35%, Series D, 1/16/96 (GIC; Bayerishe Landesbank)....................                        7,000,000           7,000,000
MISSOURI-2.7%
Mexico Industrial Development Authority, Industrial Revenue, VRDN
    (Optec DD USA Inc. Project) 4.275% (LOC; Industrial Bank of Japan) (a,b)                        7,000,000           7,000,000
NEW JERSEY-.9%
New Jersey Housing and Mortgage Finance Agency, Revenue (Statewide Mortgage)
    4.20%, Series 1, 9/29/95 (LOC; Bayerische Landesbank) (b)...............                        2,460,000           2,460,000
OKLAHOMA-6.2%
Broken Arrow Economic Development Authority, Industrial Development, VRDN
    (Paragon Films Inc. Project) 4.40% (LOC; Fuji Bank) (a,b)...............                        7,780,000           7,780,000
Tulsa County Industrial Authority, Health Care Revenue (Laureate Psychiatric
Project)
    4.40%, 6/15/95 (SBPA; William K. Warren Foundation).....................                        8,335,000           8,335,000
OREGON-.9%
State of Oregon, EDR, VRDN (Toyo Tanso USA)
    4.275%, Series CXLVII (LOC; Bank of Tokyo) (a,b)........................                        2,200,000           2,200,000
SOUTH CAROLINA-3.4%
South Carolina Jobs Economic Development Authority, EDR, VRDN
    (Saint Francis Hospital) 4.40% (LOC; Chemical Bank) (a,b)...............                        8,700,000           8,700,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                     MAY 31, 1995 (UNAUDITED)

                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT              VALUE
                                                                                                --------------      --------------
TENNESSEE-1.2%

Morristown Industrial Development Board, PCR, VRDN
    (Camvac International Inc. Project) 4.175% (LOC; Bankers Trust) (a,b)...                    $   3,000,000       $   3,000,000
TEXAS-19%
Brazos River Harbor Naval District, Harbor Revenue, VRDN (Dow Chemical Co.
Project)
    4.50%, Series A (Corp. Guaranty; Dow Chemical Co.) (a)..................                        9,700,000           9,700,000
Dallas County 3.60%, 6/15/95 (BPA; Sanwa Bank)..............................                        5,000,000           5,000,000
Greater East Texas Higher Education Authority Inc., Student Loan Revenue,
VRDN
    4.10%, Series B (LOC; Student Loan Marketing Association) (a,b).........                        7,500,000           7,500,000
Harris County Industrial Development Corp., IDR, VRDN
    (Nippon Pigment USA Inc. Project) 4.40% (LOC; Industrial Bank of Japan) (a,b)                   5,500,000           5,500,000
City of Houston Independent School District, TRAN 4.50%, 8/31/95............                        9,600,000           9,609,924
San Antonio Housing Finance Corp., MFHR, VRDN (Sunrise Apartments Project)
    4.15% (LOC; Swiss Bank Corp.) (a,b).....................................                        5,000,000           5,000,000
State of Texas, TRAN 5%, 8/31/95............................................                        7,000,000           7,007,146
VIRGINIA-6.2%
Chesapeake Industrial Development Authority, IDR, VRDN (Sumitomo Machine Co.)
    4.40% (LOC; Sumitomo Bank) (a,b)........................................                        4,000,000           4,000,000
Newport News Redevelopment and Housing Authority, MFHR, VRDN (Harbours
    Association Project) 4.65% (Surety Bond; Fireman's Fund Mortgage Corp.) (a)                     8,625,000           8,625,000
Pendleton County, IDR, VRDN (Greer Steel Project)
    4.45% (LOC; Pittsburgh National Bank) (a,b).............................                        3,400,000           3,400,000
WEST VIRGINIA-1.5%
Marion County, Community Solid Waste Disposal Facility Revenue, VRDN
    (Granttown Project) 4.30%, Series B (LOC; National Westminster Bank) (a,b)                      4,000,000           4,000,000
                                                                                                                     -------------
TOTAL INVESTMENTS (cost $259,921,293).......................................                                         $259,921,293
                                                                                                                     =============

</TABLE>

<TABLE>
<CAPTION>


GENERAL MUNICIPAL MONEY MARKET FUND, INC.

SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>     <C>
BPA           Bond Purchase Agreement                            MBIA    Municipal Bond Investors Assurance
EDR           Economic Development Revenue                                   Insurance Corporation
FGIC          Financial Guaranty Insurance Company               MFHR    Multi-Family Housing Revenue
GIC           Guaranteed Investment Contract                     PCR      Pollution Control Revenue
GO            General Obligation                                 SBPA    Standby Bond Purchase Agreement
HR            Hospital Revenue                                   SWDR    Solid Waste Disposal Revenue
IDR           Industrial Development Revenue                     TRAN    Tax and Revenue Anticipation Notes
LOC           Letter of Credit                                   VRDN    Variable Rate Demand Notes
LOR           Limited Obligation Revenue
</TABLE>

<TABLE>
<CAPTION>

SUMMARY OF COMBINED RATINGS (UNAUDITED)
FITCH (C)              OR          MOODY'S             OR         STANDARD & POOR'S           PERCENTAGE OF VALUE
- --------                           --------                       ------------------         ---------------------
<S>                                <C>                            <S>                              <C>
F1+/F1                             VMIG1/MIG1, P1 (d)             SP1+/SP1, A1+/A1 (d)              94.2%
AAA/AA (e)                         Aaa/Aa (e)                     AAA/AA (e)                         5.8
                                                                                                   -------
                                                                                                   100.0%
                                                                                                   =======
</TABLE>

NOTES TO STATEMENT OF INVESTMENTS:
    (a)  Securities payable on demand.  The interest rate, which is subject
    to change, is based upon bank prime rates or an index of market interest
    rates.
    (b)  Secured by letters of credit.  At May 31, 1995, 50.7% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, brokerage firms and government agencies.
    (c)  Fitch currently provides creditworthiness information for a limited
    number of investments.
    (d)  P1 and A1 are the highest ratings assigned tax-exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (e)  Notes which are not F, MIG or SP rated are represented by bond
    ratings of the issuers.



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

<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                       MAY 31, 1995 (UNAUDITED)
<S>                                                                                               <C>                <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                         $259,921,293
    Interest receivable.....................................................                                            2,579,498
    Prepaid expenses........................................................                                               82,457
                                                                                                                     -------------
                                                                                                                      262,583,248
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                      $   109,992
    Due to Custodian........................................................                        2,291,325
    Accrued expenses and other liabilities..................................                           61,979           2,463,296
                                                                                                  ------------       -------------
NET ASSETS..................................................................                                         $260,119,952
                                                                                                                     =============
REPRESENTED BY:
    Paid-in capital.........................................................                                         $260,413,166
    Accumulated net realized (loss) on investments..........................                                             (293,214)
                                                                                                                     -------------
NET ASSETS at value ........................................................                                         $260,119,952
                                                                                                                     =============
Shares of Common Stock Outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                          259,286,102
                                                                                                                     =============
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                            1,127,064
                                                                                                                     =============
NET ASSETS VALUE per share:
    Class A Shares
      ($258,992,892 / 259,286,102 shares)...................................                                                $1.00
                                                                                                                            ======
    Class B Shares
      ($1,127,060 / 1,127,064 shares).......................................                                                $1.00
                                                                                                                            ======

</TABLE>

<TABLE>
<CAPTION>


STATEMENT OF OPERATIONS                                                               SIX MONTHS ENDED MAY 31, 1995 (UNAUDITED)
<S>                                                                                               <C>               <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                        $   5,737,292
    EXPENSES:
      Management fee-Note 2(a)..............................................                      $   701,753
      Shareholder servicing costs-Note 2(c).................................                           98,500
      Registration fees.....................................................                           35,262
      Professional fees.....................................................                           28,336
      Directors' fees and expenses-Note 2(d)................................                           16,144
      Custodian fees........................................................                           11,640
      Prospectus and shareholders' reports..................................                            5,940
      Distribution fees (Class B shares)-Note 2(b)..........................                               18
      Miscellaneous.........................................................                            4,759
                                                                                                  ------------
          TOTAL EXPENSES....................................................                                              902,352
                                                                                                                    --------------
INVESTMENT INCOME-NET.......................................................                                            4,834,940
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                               (9,153)
                                                                                                                    --------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                        $   4,825,787
                                                                                                                    ==============
See independent accountants' review report and notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>


GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                               YEAR ENDED         SIX MONTHS ENDED
                                                                                               NOVEMBER 30,         MAY 31, 1995
                                                                                                   1994             (UNAUDITED)
                                                                                             -----------------  ------------------
<S>                                                                                           <C>                <C>
OPERATIONS:
    Investment income-net...............................................                      $     7,191,020    $      4,834,940
    Net realized gain (loss) on investments.............................                               51,495              (9,153)
    Net unrealized (depreciation) on investments for the period.........                              (29,296)            ---
                                                                                             -----------------  ------------------
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..........                            7,213,219           4,825,787
                                                                                             -----------------  ------------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares....................................................                           (7,191,020)         (4,834,636)
      Class B shares....................................................                                ---                  (304)
                                                                                             -----------------  ------------------
          TOTAL DIVIDENDS...............................................                           (7,191,020)         (4,834,940)
                                                                                             -----------------  ------------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares....................................................                        1,852,847,565         935,496,364
      Class B shares....................................................                                ---             1,128,569
    Dividends reinvested:
      Class A shares....................................................                            6,252,692           4,306,024
      Class B shares....................................................                                ---                   156
    Cost of shares redeemed:
      Class A shares....................................................                       (1,916,558,825)       (975,511,212)
      Class B shares....................................................                                ---                (1,661)
                                                                                             -----------------  ------------------
          (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS......                          (57,458,568)        (34,581,760)
                                                                                             -----------------  ------------------
            TOTAL (DECREASE) IN NET ASSETS..............................                          (57,436,369)        (34,590,913)
NET ASSETS:
    Beginning of period.................................................                          352,147,234         294,710,865
                                                                                             -----------------  ------------------
    End of period.......................................................                     $    294,710,865     $   260,119,952
                                                                                             =================  ==================

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


<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Common Stock 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      PERIOD ENDED
                                                      YEAR ENDED NOVEMBER 30,                MAY 31, 1995        MAY 31, 1995
                                      ---------------------------------------------------
PER SHARE DATA:                        1990       1991       1992      1993        1994       (UNAUDITED)       (UNAUDITED)(1)
                                      --------- ---------   --------- --------- ---------- -----------------  -----------------
    <S>                               <C>       <C>         <C>       <C>       <C>            <C>                <C>
    Net asset value, beginning
      of period...................    $  .9976  $  .9977    $  .9981  $  .9991  $  .9991       $  .9990           $1.0000
                                      --------- ---------   --------- --------- ---------      ----------         -----------
    INVESTMENT OPERATIONS:
    Investment income-net.........       .0538     .0428       .0271     .0208     .0225          .0172             .0058
    Net realized and unrealized
      gain (loss) on investments         .0001     .0004       .0010      --      (.0001)        (.0001)                --
                                      --------- ---------   --------- --------- ---------      ----------         -----------
      TOTAL FROM INVESTMENT
          OPERATIONS..............       .0539     .0432       .0281     .0208     .0224          .0171             .0058
                                      --------- ---------   --------- --------- ---------      ----------         -----------
    DISTRIBUTIONS;
    Dividends from investment
      income-net..................      (.0538)   (.0428)     (.0271)   (.0208)   (.0225)        (.0172)           (.0058)
                                      --------- ---------   --------- --------- ---------      ----------         -----------
    Net asset value, end of period     $ .9977   $ .9981     $ .9991   $ .9991   $ .9990       $  .9989           $1.0000
                                      ========= =========   ========= ========= =========      ==========         ===========
TOTAL INVESTMENT RETURN...........      5.51%     4.36%       2.74%     2.10%     2.27%          3.47%(2)          3.41%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average
      net assets..................       .62%      .62%        .64%      .63%      .64%           .64%(2)          1.21%(2)
    Ratio of net investment income
      to average net assets.......      5.39%     4.30%       2.71%     2.08%     2.22%          3.44%(2)         3.33%(2)
    Net Assets, end of period
      (000's Omitted).............    $352,320  $342,595     $397,912 $352,147  $294,711         $258,993           $1,127

(1)    From March 31, 1995 (commencement of initial offering) to May 31, 1995.
(2)    Annualized.


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


GENERAL MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a diversified open-end management investment company. Premier Mutual Fund
Services, Inc. (the "Distributor") acts as the distributor of the Fund's
shares, which are sold to the public without a sales load. The Distributor,
located at One Exchange Place, Boston, Massachusetts 02109, is a wholly-owned
subsidiary of FDI Distribution Services, Inc., a provider of mutual fund
administration services, which in turn is a wholly-owned subsidiary of FDI
Holdings, Inc., the parent company of which is Boston Institutional Group,
Inc. The Dreyfus Corporation ("Manager") serves as the Fund's investment
adviser. The Manager is a direct subsidiary of Mellon Bank, N.A.
    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.
    On May 26, 1994, the Fund's Board of Directors approved an amendment to
the Fund's Charter to provide for the issuance of additional shares of the
Fund. The amendment was approved by Fund shareholders on August 3, 1994.
Pursuant to the amendment, the Fund's existing authorized shares were
classified as Class A shares and one billion newly authorized shares of the
Common Stock of the Fund, par value $.01 per share, were classified as Class
B shares. The Fund began offering both Class A and Class B shares on March
31, 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.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Directors 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.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain are normally declared and paid
annually, but the Fund may make distributions on a more frequent basis to
comply with the distribution requirements of the Internal Revenue Code. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

    The Fund has an unused capital loss carryover of approximately $284,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1994. If not
applied, $281,000 expires in fiscal 1995 and $3,000 expires in fiscal 1998.
    At May 31, 1995, 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 1/2 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, interest on borrowings, brokerage
commissions 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 May 31, 1995.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, effective
March 31, 1995, the Fund directly bears the costs 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 .20% of
the value of the average daily net assets of Class B. From March 31, 1995
through May 31, 1995, $18 was 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 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 May 31, 1995, the Fund was charged an
aggregate of $45,059 pursuant to the Class A Shareholder Services Plan.
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), effective March 31, 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 maintenance of shareholder
accounts. The Distributor may make payments to service agents in respect of
these services. The Distributor determines the amounts to be paid to service
agents. From March 31, 1995 through May 31, 1995, $23 was charged to Class B
shares by the Distributor pursuant to the Class B Shareholder Services Plan.
    (D) Each director 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 $500
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
    We have reviewed the accompanying statement of assets and liabilities of
General Municipal Money Market Fund, Inc., including the statement of
investments, as of May 31, 1995, and the related statements of operations and
changes in net assets and financial highlights for the six month period ended
May 31, 1995. 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
November 30, 1994 and financial highlights for each of the five years in the
period ended November 30, 1994 and in our report dated January 3, 1995, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.

(Ernst & Young LLP  Signature Logo)

New York, New York
July 7, 1995



GENERAL MUNICIPAL
MONEY MARKET FUND, INC.
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
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940




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




Printed in U.S.A.                        697/918SA955
General Municipal
Money Market
Fund, Inc.
Semi-Annual Report
May 31, 1995



(Dreyfus Logo)



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