GENERAL MUNICIPAL MONEY MARKET FUND INC
N-30D, 1994-07-27
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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 period ended May 31, 1994,
the annualized yield provided by your Fund was 1.96%. After taking into
account the effect of compounding, the annualized effective yield was 1.98%.*
Income dividends of approximately $.01 per share paid during the period were
exempt from Federal income tax.**
    At our last reporting, we were keeping a watchful eye on the status of
the U.S. economy, the direction of interest rates and any significant
variation in inflationary indicators. Early in the period, economic numbers
hinted that the nation's growth might be more anemic than anticipated. With
no strong threat of a rekindling of inflation, the municipal market responded
by providing some of the lowest historic yields in both the bond and money
markets. In a somewhat unusual turn of events, assets of municipal money
market funds increased despite the unprecedented low yield environment.
    In the first half of 1994, however, signs of economic strength began to
emerge along with the specter of a tighter Federal Reserve Board policy.
Through a series of tightening moves between February 4 and May 17, the Fed
signaled its desire to choke off inflationary pressures before they had an
opportunity to build significantly. In a step-by-step process through the
first four months of the year, the Fed inched up the Federal Funds rate by 75
basis points to its current 3.75% level. The bond market responded with an
uneasy 100 basis point rise in rates, with short-term rates moving upward by
50 basis points. The most overt move came on May 17 when the Fed raised both
the discount rate and the Federal Funds rate by 50 basis points, to 3.50% and
4.25% respectively. The moves appeared to reach a neutral monetary policy,
clearly signaling the end of the Fed's 1993 accommodative stance.
    With these changes in the Federal Reserve's monetary stance, uneasiness
in other markets served to bolster rates in the short-term municipal market
as cash moved into municipal money markets from both equity and bond funds.
Short-term municipal rates increased, but to a lesser degree than their
taxable counterparts. Total net assets of short-term municipal funds reached
an all-time high of over $119 billion, which declined as the tax season
arrived. Traditionally, money market funds lose assets during this time of
year as investors tap their money to pay income taxes. During this period,
municipal notes continued to provide attractive returns relative to
comparable taxable alternatives.
    In the coming weeks and months, we will sort through the various
financings which generally flood the market during the late spring and early
summer, to obtain those issues we feel represent the best values for your
portfolio while maintaining our high quality standards and high degree of
liquidity. We will adjust our strategy to respond to changes in the market
and in Federal Reserve policy and to any implementation of the proposed
changes in the regulations governing money market funds which we have received
 from the Securities and Exchange Commission. We will keep you informed in
future letters as to the effect these various changes may have on the tax
exempt market and how they will affect our portfolio strategy.
    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,
                              (Signature Logo)
                              Richard J. Moynihan
                              President
June 16, 1994
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, 1994 (UNAUDITED)

                                                                                           PRINCIPAL
TAX EXEMPT INVESTMENTS--100.0%                                                                AMOUNT            VALUE
                                                                                      ---------------       --------------
<S>                                                                                   <C>                    <C>
ARIZONA--4.0%
Arizona Educational Loan Marketing Corp., Educational Loan Revenue, VRDN
    3%, Series A (Insured; MBIA) (a)........................................          $       6,500,000       $    6,500,000
Glendale Industrial Development Authority, HR, VRDN
    (West Valley Camelback) 2.85% (LOC; Citibank) (a,b).....................                  6,800,000            6,800,000
CALIFORNIA--7.0%
State of California, RAW 3.75%, Series A, 12/21/94..........................                  8,000,000            8,013,195
California Higher Education Loan Authority Inc., Student Loan Revenue,
    Refunding (Senior Lien) 3.60%, Series A-2, 5/1/95
    (LOC; Student Loan Marketing Association)(b)............................                  7,500,000            7,500,000
California School Cash Reserve Program Authority, Notes 3.40%, 7/5/94.......                  8,000,000            8,003,614
COLORADO--2.8%
Colorado Student Obligation Bond Authority, Student Loan Revenue, VRDN
    3.10%, Series A (LOC; Sumitomo Bank) (a,b)..............................                  3,700,000            3,700,000
Denver Urban Renewal Authority, Tax Increment Revenue (Downtown Denver
Renewal)
    3.15%, Series A, 9/8/94 (Collateralized In; U.S. Treasury Bills)........                  5,700,000            5,700,000
DELAWARE--.8%
Delaware Economic Development Authority, IDR, VRDN (Orient Chemical Corp.
Project)
    3.25% (LOC; Sumitomo Bank) (a,b)........................................                  2,700,000            2,700,000
DISTRICT OF COLUMBIA--8.5%
District of Columbia:
    General Fund Recovery, VRDN 3.20%, Series B-3 (LOC; Industrial Bank of Japan) (a,b)       8,800,000            8,800,000
    TRAN 3.50%, Series A, 9/30/94 (LOC; Swiss Bank Corp.) (b)...............                 15,000,000           15,031,885
    VRDN, Refunding 3%, Series A-4 (LOC; Industrial Bank of Japan) (a,b)....                  4,800,000            4,800,000
FLORIDA--.8%
Lee County Industrial Development Authority, IDR, VRDN
    (The Christian and Missionary Alliance Foundation-Shell Point Village
Project)
    2.875% (LOC; Banque Nationale de Paris) (a,b)...........................                  2,860,000           2,860,000
HAWAII--2.7%
City and County of Honolulu, MFHR, VRDN (Halekua Gardens Project)
    3.55%, Series A (LOC; Bank of Tokyo) (a,b)..............................                  9,086,000           9,086,000
ILLINOIS--8.2%
City of Chicago:
    3.15%, Series B, 10/31/94 (BPA: Dai-Ichi Kangyo Bank, Industrial Bank of
Japan,
      Mitsubishi Bank, Sanwa Bank and Sumitomo Bank)........................                 10,000,000           10,000,000
    Gas Supply Revenue (People's Gas Light and Coke Co.)
      2.55%, Series B, 12/1/94..............................................                  9,000,000            9,000,000
Chicago O'Hare International Airport, Revenue, VRDN (General Airport Second
Lien)
    3.15%, Series A (LOC; Sanwa Bank) (a,b).................................                  2,300,000            2,300,000
City of West Chicago, IDR, VRDN (Acme Printing Ink Project)
    3.125% (LOC; Bank of Tokyo) (a,b).......................................                  6,000,000            6,000,000
INDIANA--2.4%
Indiana Bond Bank, Advanced Funding Program, Notes 3.03%, Series A-2, 1/17/95                 8,000,000            8,013,699

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                         MAY 31, 1994 (UNAUDITED)

                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            AMOUNT            VALUE
                                                                                      ---------------       --------------
IOWA--1.5%
Iowa Financial Authority, Small Business Development, MFHR, VRDN
    (Village Court Association) 2.875%, Series B (LOC; Bankers Trust) (a,b).             $    5,000,000       $    5,000,000
KENTUCKY--1.4%
Boone County, IDR, VRDN (Curtain Matheson Scientific) 3.40% (LOC; Barclays
Bank) (a,b)................................................................                   2,500,000            2,500,000
Davies County, Solid Waste Disposal Facility Revenue, VRDN (Scott Paper Co.
Project)
    3.15%, Series B (LOC; ABN-Amro Bank) (a,b)..............................                    500,000              500,000
City of Georgetown, Public Project Revenue, VRDN 3.30% (LOC; Bank of Tokyo) (a,b)             1,720,000            1,720,000
LOUISIANA--7.5%
Jefferson Parish Hospital Service District Number 2, HR, VRDN
    2.85% (LOC; Mitsubishi Bank) (a,b)......................................                 15,000,000           15,000,000
Louisiana Offshore Terminal Authority, Deepwater Port Revenue, VRDN,
Refunding
    (Loop Inc.-First Stage) 3.10% (LOC; Union Bank of Switzerland) (a,b)....                  7,000,000            7,000,000
Saint Charles Parish, PCR, VRDN (Shell Oil Project) 3.10%, Series A (a).....                  3,000,000            3,000,000
MICHIGAN--3.2%
Macomb Township Economic Development Corp., LOR, VRDN (ACR Industries
Project)
    3.10% (LOC; Comerica Bank) (a,b)........................................                  1,050,000            1,050,000
Michigan Housing Development Authority, LOR, Refunding, VRDN
    (Harbortown Limited Divide) 2.925% (LOC; Bankers Trust) (a,b)...........                  6,000,000            6,000,000
Michigan Strategic Fund, Solid Waste Disposal Revenue, VRDN
    (Grayling Generating Project) 3.20% (LOC; Barclays Bank) (a,b)..........                  3,800,000            3,800,000
MINNESOTA--2.1%
Minnesota Housing Finance Agency, SFMR Bonds
    2.50%, Series F, 1/12/95 (GIC; Societe Generale)........................                  7,000,000            7,000,000
MISSOURI--2.1%
Mexico Industrial Development Authority, Industrial Revenue, VRDN
    (Optec DD USA Inc. Project) 3.125% (LOC; Industrial Bank of Japan) (a,b)                  7,000,000            7,000,000
OHIO--1.5%
Ohio Housing Finance Agency, SFMR 2.95%, Series A-2, 6/1/94
    (GIC; Goldman, Sachs and Co.)...........................................                  5,000,000            5,000,000
OKLAHOMA--4.6%
Broken Arrow Economic Development Authority, Industrial Revenue, VRDN
    (Paragon Films Inc. Project) 3.25% (LOC; Fuji Bank) (a,b)...............                  7,780,000            7,780,000
Tulsa County Industrial Authority, Health Care Revenue (Laureate Psychiatric
Project)
    2.40%, 6/15/94 (SBPA; William K. Warren Foundation).....................                  7,500,000            7,500,000
OREGON--3.6%
City of Klamath Falls, Electric Revenue (Salt Caves Hydroelectric)
    3.75%, Series A, 5/2/95 (Escrowed In; U.S. Treasury Bills)..............                 10,000,000           10,000,000
State of Oregon, EDR, VRDN (Toyo Tanso USA)
    3.125%, Series CXLVII (LOC; Bank of Tokyo) (a,b)........................                  2,200,000            2,200,000
PENNSYLVANIA--.9%
Upper Allegheny Joint Sanitation Authority, Electric Revenue (Allegheny
Valley)
    2.81%, Series B, 7/15/94 (GIC; American International Group)............                  3,000,000            3,000,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                              MAY 31, 1994 (UNAUDITED)

                                                                                            PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            AMOUNT            VALUE
                                                                                      ---------------       --------------
TENNESSEE--.9%
Morristown Industrial Development Board, PCR, VRDN
    (Camvac International Inc. Project) 3.175% (LOC; ABN-Amro Bank) (a,b)...             $    3,000,000       $    3,000,000
TEXAS--20.5%
Brazos Higher Education Authority Inc., Student Loan Revenue, VRDN
    3% (LOC; National Australia Bank) (a,b).................................                 14,000,000           14,000,000
Brazos River Harbor Naval District, Harbor Revenue, VRDN (Dow Chemical Co.
Project)
    3.20%, Series A (Corp. Guaranty; Dow Chemical Co.) (a)..................                  9,700,000            9,700,000
Dallas County 2.70%, 6/15/94 (BPA; Sanwa Bank)..............................                  5,000,000            5,000,000
Greater East Texas Higher Education Authority Inc., Student Loan Revenue,
VRDN
    3.20%, Series B (LOC; Student Loan Marketing Association) (a,b).........                  7,500,000            7,500,000
Gulf Coast Industrial Development Authority, Marine Terminal Revenue, VRDN
    (Amoco Oil Co. Project) 3.10% (Corp. Guaranty; Amoco Credit Corp.) (a)..                  9,200,000            9,200,000
Harris County, VRDN (Toll Road Unlimited Tax-Sublien)
    2.75%, Series D (SBPA; Sumitomo Bank) (a)...............................                  3,000,000            3,000,000
Harris County Industrial Development Corp., IDR, VRDN
    (Nippon Pigment USA Inc. Project) 3.25% (LOC; Industrial Bank of Japan) (a,b)             5,500,000            5,500,000
San Antonio Housing Finance Corp., MFHR, VRDN (Sunrise Apartments Project)
    2.95% (LOC; Swiss Bank Corp.) (a,b).....................................                  5,000,000            5,000,000
State of Texas, TRAN 3.25%, 8/31/94.........................................                  6,600,000            6,615,376
Trinity River Industrial Development Authority, IDR, VRDN
    (Toys 'R' Us) 2.875% (LOC; Bankers Trust) (a,b).........................                  3,000,000            3,000,000
UTAH--3.0%
Intermountain Power Agency, Power Supply Revenue, CP
    2.75%, Series E, 6/15/94 (SBPA; Industrial Bank of Japan)...............                 10,000,000           10,000,000
VIRGINIA--6.6%
Chesapeake Industrial Development Authority, IDR, VRDN (Sumitomo Machine Co.)
    3.25% (LOC; Sumitomo Bank) (a,b)........................................                  4,000,000            4,000,000
Newport News Redevelopment and Housing Authority, MFHR, VRDN
    (Harbours Association Project) 3.05% (Surety Bond; Fireman's Fund
Mortgage Corp.) (a).........................................................                  8,625,000            8,625,000
Pendleton County, IDR, VRDN (Greer Steel Project)
    3.15% (LOC; Pittsburgh National Bank) (a,b).............................                  3,600,000            3,600,000
Virginia Housing Development Authority (Series A-Subseries A-Stem)
    3.10%, 12/15/94.........................................................                  6,000,000            6,000,000
WEST VIRGINIA--1.2%
Marion County, Community Solid Waste Disposal Facility Revenue, VRDN
    (Granttown Project) 2.95%, Series B (LOC; National Westminster Bank) (a,b)                4,000,000            4,000,000
WISCONSIN--1.5%
City of Milwaukee, RAN 3.50%, Series A, 2/23/95.............................                  5,000,000            5,017,751
WYOMING--.7%
Wyoming Community Development Authority (Single Family Mortgage)
    2.80%, Series D, 10/27/94 (Escrowed In; U.S. Government Securities).....                  2,350,000            2,350,000
                                                                                                               -------------
TOTAL INVESTMENTS (cost $334,966,520).......................................                                    $334,966,520
                                                                                                                ============
</TABLE>
<TABLE>
<CAPTION>
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>     <C>
BPA           Bond Purchase Agreeement                           MFHR    Multi-Family Housing Revenue
CP            Commercial Paper                                   PCR     Pollution Control Revenue
EDR           Economic Development Revenue                       RAN     Revenue Anticipation Notes
GIC           Guaranteed Investment Contract                     RAW     Revenue Anticipation Warrants
HR            Hospital Revenue                                   SBPA    Standby Bond Purchase Agreeement
IDR           Industrial Development Revenue                     SFMR    Single Family Mortgage Revenue
LOC           Letter of Credit                                   TRAN    Tax and Revenue Anticipation Notes
LOR           Limited Obligation Revenue                         VRDN    Variable Rate Demand Notes
MBIA          Municipal Bond Insurance Association
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF COMBINED RATINGS (UNAUDITED)
MOODY'S                OR          STANDARD & POOR'S                 PERCENTAGE OF VALUE
- ---------                          --------------------           -----------------------
<S>                                <C>                                    <S>
VMIG1/MIG1, P1 (c)                 SP1+/SP1, A1+/A1 (c)                   94.6%
Aaa/Aa (d)                         AAA/AA (d)                              5.4%
                                                                        -------
                                                                         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, 1994, 51.9% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, brokerage firms 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.


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, 1994 (UNAUDITED)
ASSETS:
    <S>                                                                                        <C>           <C>
    Investments in securities, at value--Note 1(a)..........................                                 $334,966,520
    Cash....................................................................                                    7,842,653
    Interest receivable.....................................................                                    1,935,787
    Prepaid expenses........................................................                                       47,408
                                                                                                           --------------
                                                                                                              344,792,368
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                   $149,770
    Accrued expenses and other liabilities..................................                     80,078           229,848
                                                                                              -----------  --------------
NET ASSETS  ................................................................                                 $344,562,520
                                                                                                            =============
REPRESENTED BY:
    Paid-in capital.........................................................                                 $344,828,525
    Accumulated net realized (loss) on investments..........................                                     (266,005)
                                                                                                           --------------
NET ASSETS at value applicable to 344,828,525 outstanding shares of
    Common Stock, equivalent to $1.00 per share (15 billion shares of
    $.01 par value authorized)..............................................                                $344,562,520
                                                                                                            =============
STATEMENT OF OPERATIONS                                                   SIX MONTHS ENDED MAY 31, 1994 (UNAUDITED)
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                               $    4,567,216
    EXPENSES:
      Management fee--Note 2(a).............................................                   $877,936
      Shareholder servicing costs_Note 2(b).................................                    132,070
      Registration fees.....................................................                     39,154
      Professional fees.....................................................                     20,182
      Custodian fees........................................................                     18,149
      Prospectus and shareholders' reports..................................                     16,405
      Directors' fees and expenses_Note 2(c)................................                     13,788
      Miscellaneous.........................................................                      9,078
                                                                                             ----------
          TOTAL EXPENSES....................................................                                    1,126,762
                                                                                                           --------------
          INVESTMENT INCOME--NET............................................                                    3,440,454
REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
    Net realized gain on investments........................................                  $  69,550
    Net unrealized (depreciation) on investments............................                    (29,296)
                                                                                              ----------
          NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS...................                                       40,254
                                                                                                           --------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                               $    3,480,708
                                                                                                           ==============



See independent accountants' review report and notes to financial statements.
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                        YEAR ENDED      SIX MONTHS ENDED
                                                                                       NOVEMBER 30,        MAY 31, 1994
                                                                                           1993            (UNAUDITED)
                                                                                    -----------------    -----------------
OPERATIONS:
    Investment income--net...............................................            $     7,614,307     $     3,440,454
    Net realized gain on investments.....................................                     15,730              69,550
    Net unrealized appreciation (depreciation) on investments for the period                  29,296            (29,296)
                                                                                     --------------      ---------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS...............                  7,659,333           3,480,708
                                                                                     --------------      ---------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income--net...............................................                 (7,614,307)         (3,440,454)
                                                                                     --------------      ---------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold........................................              2,320,677,058         990,324,678
    Dividends reinvested.................................................                  6,135,940           2,858,677
    Cost of shares redeemed..............................................             (2,372,623,110)     (1,000,808,323)
                                                                                     --------------      ---------------
      (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS...........                (45,810,112)         (7,624,968)
                                                                                     --------------      ---------------
          TOTAL (DECREASE) IN NET ASSETS.................................                (45,765,086)         (7,584,714)
NET ASSETS:
    Beginning of period..................................................               397,912,320          352,147,234
                                                                                     --------------      ---------------
    End of period........................................................             $ 352,147,234        $ 344,562,520
                                                                                     ==============        =============




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.

                                                                    YEAR ENDED NOVEMBER 30,                    SIX MONTHS ENDED
                                                        ---------------------------------------------------       MAY 31, 1994
PER SHARE DATA:                                            1989       1990       1991       1992       1993       (UNAUDITED)
                                                        -------    --------   --------   --------   --------    -------------
    <S>                                                  <C>         <C>        <C>       <C>         <C>            <C>
    Net asset value, beginning of period...              $.9977      $.9976     $.9977    $.9981      $.9991         $.9991
                                                        -------    --------   --------   --------   --------    -------------
    INVESTMENT OPERATIONS:
    Investment income--net.................              .0574        .0538     .0428      .0271       .0208         .0098
    Net realized and unrealized gain (loss)
      on investments.......................             (.0001)       .0001     .0004      .0010         -_          .0001
                                                        -------    --------   --------   --------   --------    -------------
      TOTAL FROM INVESTMENT OPERATIONS.....             .0573         .0539     .0432      .0281       .0208         .0099
                                                        -------    --------   --------   --------   --------    -------------
    DISTRIBUTIONS;
    Dividends from investment income--net..            (.0574)      (.0538)    (.0428)   (.0271)     (.0208)        (.0098)
                                                        -------    --------   --------   --------   --------    -------------
    Net asset value, end of period.........            $.9976       $.9977    $.9981    $.9991       $.9991        $.9992
                                                       =======    ========    ========   =======   =========   ==============
TOTAL INVESTMENT RETURN                                5.89%        5.51%     4.36%     2.74%        2.10%         1.97%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets             .64%        .62%       .62%     .64%          .63%         .64%*
    Ratio of net investment income to average
      net assets...........................            5.74%      5.39%       4.30%    2.71%         2.08%        1.96%*
    Net Assets, end of period (000's Omitted)       $343,917    $352,320   $342,595  $397,912    $352,147     $344,563
* 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. Dreyfus Service
Corporation ("Distributor") acts as the exclusive distributor of the Fund's
shares, which are sold to the public without a sales charge. The Distributor
is a wholly-owned subsidiary of The Dreyfus Corporation ("Manager").
    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.
    (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, when appropriate, 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 taxes.
    The Fund has an unused capital loss carryover of approximately $336,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1993. If not
applied, $333,000 expires in fiscal 1995 and $3,000 expires in fiscal 1998.
    At May 31, 1994, 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, 1994.
    (B) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
the Distributor an amount not to exceed an annual rate of .25 of 1% of the
value of the Fund's average daily net assets for servicing shareholder
accounts. The services provided may include personal services relating to
shareholder accounts,
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
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, 1994, the Fund was
charged an aggregate of $38,761 pursuant to the Shareholder Services Plan.
    (C) Certain officers and directors of the Fund are "affiliated persons,"
as defined in the Act, of the Manager and/or the Distributor. Each director
who is not an "affiliated person" receives an annual fee of $2,500 and an
attendance fee of $500 per meeting.
    (D) On December 5, 1993, the Manager entered into an Agreement and Plan
of Merger (the "Merger Agreement") providing for the merger of the Manager
with a subsidiary of Mellon Bank Corporation ("Mellon").
    Following the merger, it is planned that the Manager will be a direct
subsidiary of Mellon Bank, N.A. Closing of this merger is subject to a number
of contingencies, including receipt of certain regulatory approvals and
approvals of the stockholders of the Manager and of Mellon. The merger is
expected to occur in August 1994, but could occur later.
    As a result of regulatory requirements and the terms of the Merger
Agreement, the Manager will seek various approvals from the Fund's
shareholders before completion of the merger. Proxy materials, approved by
the Fund's Board, recently have been mailed to Fund shareholders.
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
REVIEW REPORT OF ERNST & YOUNG, 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, 1994, and the related statements of operations and
changes in net assets and financial highlights for the six month period ended
May 31, 1994. 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, 1993 and financial highlights for each of the five years in the
period ended November 30, 1993 and in our report dated January 7, 1994, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.


(Signature Logo)

New York, New York
July 6, 1994

"Dreyfus" Logo

General Municipal
Money Market
Fund, Inc.
Semi-Annual
Report
May 31, 1994
Dreyfus Lion picture/logo
Dreyfus "D" logo.
GENERAL MUNICIPAL
MONEY MARKET FUND, INC.
144 Glenn Curtiss Boulevard
Uniondale, NY 11556
MANAGER
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166
DISTRIBUTOR
Dreyfus Service Corporation
200 Park Avenue
New York, NY 10166
CUSTODIAN
The Bank of New York
110 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.



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