GENERAL MONEY MARKET FUND INC
N-30D, 1996-03-26
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GENERAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the General Money
Market Fund, Inc. For its annual reporting period ended January 31, 1996,
your Fund produced a yield of 5.29% per share for Class A shares and an
annualized yield of 5.08% for Class B shares from inception on March 31,
1995. Reinvesting dividends and calculating the effect of compounding
resulted in an effective yield of 5.42% for Class A shares and an annualized
effective yield of 5.20% for Class B shares.*
THE ECONOMY
    On January 31, the last day of the Fund's reporting period, the Federal
Reserve Board lowered the Federal Funds rate from 5.50% to 5.25%, which
prompted banks to lower the Prime Rate from 8.50% to 8.25%. This was the
second move for these key rates in a two-month time span. The Federal Reserve
also reduced the Discount Rate from 5.25% to 5.00%. The reduction in interest
rates was a continuation of an easing in monetary policy that has prevailed
since last July.
    Economic activity over the course of the period had fundamentally
declined. The period between the July and December rate cuts, however,
revealed a strengthening in some areas such as raw materials, finished goods,
employment and income which subsequently abated. Later, regional business
activity showed a moderate growth trend, particularly in the Northeast where
performance was adversely affected by weather-related circumstances. In the
retail sector, disappointing sales left businesses with excess inventories,
contributing to one of the worst holiday seasons in recent years. Other
sectors, including manufacturing and consumer confidence, also turned down.
The Consumer Price Index remained well under control.
    Concern arose over prolonged sluggishness that could threaten long-term
sustainable growth. Actions were taken by the Federal Reserve to accelerate
the rate of growth without sparking inflation. It is possible that if more
signs of weakness emerge to undermine economic expansion, short-term interest
rates will continue to decline. However, in early February, concerns about
inflation tempered the outlook.
MARKET ENVIRONMENT/PORTFOLIO ACTIVITY
    The gradual moderation in economic expansion and reduction of
inflationary pressures were fundamental backdrops to a positive market
environment. Solid technical factors, led by a stable dollar, increased the
participation of foreign investors. Overall domestic demand also helped the
market absorb the supply of Treasury securities and contributed to positive
market psychology throughout the period.
    Concerns over Washington's ability to formulate a balanced budget
amendment and to resolve debt ceiling limit issues affected the market
periodically throughout this reporting period. However, should low long-term
interest rates continue, they could have a favorable effect on the value of
short-term money market securities.
    Portfolio activity for your Fund centered on extending the average
maturity and seeking to enhance yield through spread evaluations and market
timing.

    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we greatly appreciate your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Sincerely,

                          [Patricia A. Larkin signature logo]

                              Patricia A. Larkin
                              Senior Portfolio Manager
February 15, 1996
New York, N.Y.
*  Effective and annualized effective yields are based upon dividends
declared daily and reinvested monthly.



<TABLE>
<CAPTION>
GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                           JANUARY 31, 1996
                                                                                                   PRINCIPAL
NEGOTIABLE BANK CERTIFICATES OF DEPOSIT-21.3%                                                       AMOUNT           VALUE
                                                                                                    _______         _______
<S>                                                                                              <C>              <C>
Bayerische Vereinsbank AG (Yankee)
    5.88%, 12/6/96..........................................................                     $  20,000,000    $ 20,000,000
Commerzbank AG (Yankee)
    6%, 2/2/96..............................................................                        10,000,000     10,000,000
Dai-Ichi Kangyo Bank Ltd. (London)
    5.82%, 3/8/96...........................................................                         5,000,000      5,000,049
Mitsubishi Bank Ltd. (London)
    5.63%, 3/12/96..........................................................                         15,000,000    15,003,239
Mitsubishi Bank Ltd. (Yankee)
    5.83%, 3/6/96...........................................................                         5,000,000      5,000,067
Rabobank Nederland N.V. (Yankee)
    5.14%, 7/1/96...........................................................                         20,000,000    20,003,163
Sanwa Bank Ltd. (Yankee)
    5.46%, 4/30/96..........................................................                         25,000,000    25,003,049
Sumitomo Bank Ltd. (Yankee)
    5.61%-5.70%, 4/2/96-4/19/96.............................................                         35,000,000    35,001,150
SwedBank (Yankee)
    5.32%, 6/26/96..........................................................                         15,000,000    15,000,000
                                                                                                                   ----------
TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT
    (cost $150,010,717).....................................................                                      $150,010,717
                                                                                                                  ============
BANKERS' ACCEPTANCE-7.6%
Bank of Tokyo Ltd. (Yankee)
    5.80%-5.82%, 3/1/96-3/6/96..............................................                      $  35,000,000    $34,822,597
Dai-Ichi Kangyo Bank Ltd. (Yankee)
    5.90%-6.00%, 2/14/96-3/11/96............................................                         19,000,000    18,934,464
                                                                                                                   ----------
TOTAL BANKERS' ACCEPTANCE
    (cost $53,757,061)......................................................                                       $53,757,061
                                                                                                                  ============

COMMERCIAL PAPER-23.7%
Bankers Trust New York Corp.
    5.42%, 7/8/96...........................................................                      $  20,000,000    $19,536,972
Den Danske Corp. Inc.
    5.20%-5.52%, 6/12/96-7/31/96............................................                         35,000,000    34,223,837
General Electric Capital Corp.
    5.40%, 6/24/96..........................................................                         9,000,000      8,810,640
General Motors Acceptance Corp.
    5.82%, 2/23/96..........................................................                         5,000,000      4,982,461
Lehman Brothers Holdings Inc.
    5.65%, 5/10/96 (a)......................................................                         10,000,000    10,000,000
Maguire/Thomas Partners Westlake/Southlake Partnership
    5.86%, 3/4/96 (b).......................................................                         10,650,000    10,595,283

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                  JANUARY 31, 1996
                                                                                                      PRINCIPAL
COMMERCIAL PAPER (CONTINUED)                                                                           AMOUNT           VALUE
                                                                                                       _______         _______
Merrill Lynch & Co. Inc.
    5.28%, 6/21/96..........................................................                      $  15,000,000    $14,696,262
NationsBank Corp.
    5.61%, 5/28/96..........................................................                         10,000,000      9,822,550
Spintab AB
    5.60%-5.86%, 3/26/96-4/16/96............................................                         35,000,000     34,664,667
SwedBank Inc.
    5.32%-5.90%, 2/20/96-7/18/96............................................                         20,000,000     19,622,279
                                                                                                                   ----------
TOTAL COMMERCIAL PAPER
    (cost $166,954,951).....................................................                                      $166,954,951
                                                                                                                  ============
CORPORATE NOTES-15.5%
Bear Stearns Companies Inc.
    5.65%-5.74%, 7/17/96-11/18/96 (a).......................................                         $20,000,000    $20,000,000
General Electric Capital Corp.
    5.76%-5.78%, 3/29/96-4/5/96 (a).........................................                         25,000,000    24,999,036
General Motors Acceptance Corp.
    5.59%, 6/7/96 (a).......................................................                         5,000,000      4,998,158
Lehman Brothers Holdings Inc.
    5.75%-5.95%, 5/16/96-1/6/97 (a).........................................                         20,000,000    20,000,000
Merrill Lynch & Co. Inc.
    5.68%-5.81%, 7/2/96-1/16/97 (a).........................................                         19,000,000    18,998,959
PHH Corp.
    5.65%, 11/12/96 (a).....................................................                         20,000,000    19,989,247
                                                                                                                   ----------
TOTAL CORPORATE NOTES
    (cost $108,985,400).....................................................                                      $108,985,400
                                                                                                                  ============
SHORT-TERM BANK NOTES-5.7%
First National Bank of Boston
    5.73%-5.77%, 6/7/96-6/24/96 (a).........................................                      $  30,000,000    $30,000,000
PNC Bank N.A.
    5.50%, 9/18/96..........................................................                         10,000,000    10,004,694
                                                                                                                   ----------
TOTAL SHORT-TERM BANK NOTES
    (cost $40,004,694)......................................................                                     $  40,004,694
                                                                                                                  ============
U.S. GOVERNMENT AGENCIES-27.0%
Federal Farm Credit Banks, Floating Rate Notes
    5.58%, 11/7/96-7/25/97 (a)..............................................                      $  25,000,000    $ 24,983,276
Federal Home Loan Banks, Floating Rate Notes
    6.08%, 1/31/97 (a)......................................................                         15,000,000     15,000,000
Federal Home Loan Mortgage Corp., Floating Rate Notes
    5.75%, 6/30/98 (a)......................................................                         10,700,000     10,729,392

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                JANUARY 31, 1996
                                                                                                    PRINCIPAL
U.S. GOVERNMENT AGENCIES (CONTINUED)                                                                 AMOUNT           VALUE
                                                                                                   __________       __________
Federal National Mortgage Association, Floating Rate Notes
    5.56%-6.09%, 9/27/96-1/21/98 (a)........................................                       $140,000,000   $139,938,815
                                                                                                                   ----------
TOTAL U.S. GOVERNMENT AGENCIES
    (cost $190,651,483).....................................................                                      $190,651,483
                                                                                                                  ============
Time Deposits - 1.7%

Berliner Handels-und Frankfurter Bank AG (London)
    5.62%, 2/1/96
    (cost $11,999,000)......................................................                        $11,999,000    $11,999,000
                                                                                                                  ============
TOTAL INVESTMENTS
    (cost $722,363,306)..........................................                   102.5%                        $722,363,306
                                                                                   =======                        =============
LIABILITIES, LESS CASH AND RECEIVABLES...........................                   (2.5%)                       $ (17,336,284)
                                                                                   =======                        =============
NET ASSETS  ................................................                        100.0%                         $705,027,022
                                                                                   =======                        =============

NOTES TO STATEMENT OF INVESTMENTS:
    (a)  Variable interest rate-subject to periodic change.
    (b)  Backed by an irrevocable letter of credit.





See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                   JANUARY 31, 1996
<S>                                                                                                <C>            <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                      $722,363,306
    Interest receivable.....................................................                                         3,683,951
    Prepaid expenses........................................................                                            58,896
                                                                                                                  -------------
                                                                                                                   726,106,153
LIABILITIES:
    Due to The Dreyfus Corporation and subsidiaries.........................                        $303,065
    Due to Distributor......................................................                         115,990
    Due to Custodian........................................................                         445,060
    Payable for investment securities purchased.............................                      20,008,919
    Accrued expenses and other liabilities..................................                          206,097         21,079,131
                                                                                                  -----------      -------------
NET ASSETS  ................................................................                                        $705,027,022
                                                                                                                   =============
REPRESENTED BY:
    Paid-in capital.........................................................                                        $705,045,716
    Accumulated net realized (loss) on investments..........................                                             (18,694)
                                                                                                                   -------------
NET ASSETS at value.........................................................                                        $705,027,022
                                                                                                                   =============
Shares of Common Stock outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                         654,600,180
                                                                                                                   =============
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                          50,445,536
                                                                                                                   =============
NET ASSET VALUE per share:
    Class A Shares
      ($654,581,139 / 654,600,180 shares)...................................                                         $1.00
                                                                                                                    ========
    Class B Shares
      ($50,445,883 / 50,445,536 shares).....................................                                         $1.00
                                                                                                                    ========





See notes to financial statements.

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                          YEAR ENDED JANUARY 31, 1996
INVESTMENT INCOME:
INTEREST INCOME.............................................................                                         $38,965,556
EXPENSES:
    Management fee-Note 2(a)................................................                      $3,172,667
    Distribution fees (Class A & B Shares)-Note 2(b)........................                       1,269,067
    Shareholder servicing costs-Note 2(c)...................................                         764,150
    Custodian fees..........................................................                         111,646
    Registration fees.......................................................                         110,350
    Professional fees.......................................................                          59,933
    Prospectus and shareholders' reports....................................                          40,231
    Directors' fees and expenses-Note 2(d)..................................                          37,465
    Miscellaneous...........................................................                          12,772
                                                                                                  -----------
          TOTAL EXPENSES....................................................                       5,578,281
    Less-reduction in shareholder servicing costs due
      to undertaking-Note 2(c)..............................................                          77,410
                                                                                                  -----------
          NET EXPENSES......................................................                                         5,500,871
                                                                                                                    -----------
INVESTMENT INCOME-NET.......................................................                                         33,464,685
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                             (3,057)
                                                                                                                    -----------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                         $33,461,628
                                                                                                                    =============





See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                                    YEAR ENDED JANUARY 31,
                                                                                              _________________________________
                                                                                                   1995               1996
                                                                                              _____________       _____________
<S>                                                                                            <C>                 <C>
OPERATIONS:
    Investment income-net.............................................                         $ 20,951,934        $33,464,685
    Net realized gain (loss) on investments...........................                                7,685             (3,057)
                                                                                              _____________       _____________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                             20,959,619        33,461,628
                                                                                              _____________       _____________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A Shares..................................................                            (20,951,934)     (32,893,579)
      Class B Shares..................................................                                 _              (571,106)
                                                                                              _____________       _____________
          TOTAL DIVIDENDS.............................................                           (20,951,934)      (33,464,685)
                                                                                              _____________       _____________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A Shares..................................................                          3,846,418,471     4,736,674,991
      Class B Shares..................................................                             _                 98,889,385
    Dividends reinvested:
      Class A Shares..................................................                             20,559,011        32,106,715
      Class B Shares..................................................                             _                     79,652
    Cost of shares redeemed:
      Class A Shares..................................................                        (3,910,940,423)    (4,686,313,457)
      Class B Shares..................................................                             _                (48,523,501)
                                                                                              _____________       _____________
          INCREASE (DECREASE) IN NET ASSETS FROM
            CAPITAL STOCK TRANSACTIONS................................                          (43,962,941)        132,913,785
                                                                                              _____________       _____________
            TOTAL INCREASE (DECREASE) IN NET ASSETS...................                           (43,955,256)        132,910,728
NET ASSETS:
    Beginning of year.................................................                           616,071,550         572,116,294
                                                                                              _____________       _____________
    End of year.......................................................                      $    572,116,294       $ 705,027,022
                                                                                              ===============      =============




See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL 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 year indicated. This information
has been derived from the Fund's financial statements.




                                                                         CLASS A SHARES                          CLASS B SHARES
                                                  __________________________________________________________     _______________
                                                                                                                   YEAR ENDED
                                                                         YEAR ENDED JANUARY 31,                    JANUARY 31,
                                                  __________________________________________________________
PER SHARE DATA:                                       1992       1993         1994         1995        1996          1996(1)
                                                     ______      ______       ______       ______     ______        __________
    <S>                                            <C>         <C>           <C>         <C>         <C>            <C>
    Net asset value, beginning of year.            $  1.00     $  1.00       $  1.00     $  1.00     $  1.00        $  1.00
                                                     ______      ______       ______       ______     ______         _______
    INVESTMENT OPERATIONS;
    Investment income-net..............               .055        .032         .025         .037       .053            .043
                                                     ______      ______       ______       ______     ______         _______
    DISTRIBUTIONS;
    Dividends from investment income-net             (.055)      (.032)       (.025)       (.037)     (.053)          (.043)
                                                     ______      ______       ______       ______     ______         _______
    Net asset value, end of year.......             $  1.00     $  1.00      $  1.00      $  1.00    $  1.00         $  1.00
                                                    ========     =======      =======     ========    =======        ========
TOTAL INVESTMENT RETURN................               5.61%      3.26%         2.56%       3.75%      5.42%           5.18%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets            .92%       .95%          .94%        .94%        .86%          1.00%(2)
    Ratio of net investment income to
      average net assets...............               5.44%      3.22%         2.53%       3.68%      5.28%           5.00%(2)
    Decrease reflected in above expense ratios
      due to undertaking by the Manager                 -          -           .02%        .04%       .01%            .07%(2)
    Net Assets, end of year (000's Omitted)        $845,690    $688,785      $616,072    $572,116    $654,581        $50,446
    (1)  From March 31, 1995 (commencement of initial offering) to January 31, 1996.
    (2)  Annualized.




See notes to financial statements.
</TABLE>
GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    General Money Market Fund, Inc. (the "Fund") is registered under the
Investment Company Act of 1940 ("Act") as a diversified open-end management
investment company. The Fund's investment objective is to provide investors
with as high a level of current income as is consistent with the preservation
of capital. The Dreyfus Corporation ("Manager") serves as the Fund's
investment adviser. The Manager is a direct subsidiary of Mellon Bank, N.A.
    Premier Mutual Fund Services, Inc. (the "Distributor") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales load. 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 for
the services offered to and the expenses borne by each class and certain
voting rights. Class A shares are subject to a Service Plan adopted pursuant
to Rule 12b-1 under the Act, 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 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 of $1.00.
    (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. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Interest
income is recognized on the accrual basis. Cost of investments represents
amortized cost.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends from investment income-net on each business day; 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, if such qualification is in the
best interests of its shareholders, by complying with the applicable
provisions of the Internal Revenue Code, and to make distributions of taxable
income sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $12,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to January 31,
1996. The carryover does not include net realized securities losses from
November 1, 1995 through

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

January 31, 1996 which are treated, for Federal
income tax purposes, as arising in fiscal 1997. If not applied, the carryover
expires in fiscal 2002.
    At January 31, 1996, the cost of investments for Federal income tax
purposes was substantially the same as the cost for financial reporting
purposes (see the Statement of Investments).
NOTE 2-MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the average
daily value of the Fund's net assets and is payable monthly. The Agreement
provides for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, interest on borrowings, brokerage
commissions and extraordinary expenses, exceed 11\2% of the average value of
the Fund's net assets for any full fiscal year. There was no expense
reimbursement for the year ended January 31, 1996, pursuant to the Agreement.
    Effective December 1, 1995, the Fund compensates Dreyfus Transfer, Inc.,
a wholly-owned subsidiary of the Manager, under a transfer agency agreement
for providing personnel and facilities to perform transfer agency services
for the Fund. Such compensation amounted to $36,359 for the period from
December 1, 1995 through January 31, 1996.
    (B) Under the Service Plan (the "Plan") with respect to Class A shares
only, adopted pursuant to Rule 12b-1 under the Act, the Fund directly bears
the costs of preparing, printing and distributing prospectuses and statements
of additional information and of implementing and operating the Plan. In
addition, the Fund reimburses (a) the Distributor for payments made for
distributing Class A shares and servicing shareholder accounts ("Servicing")
and (b) the Manager, Dreyfus Service Corporation, a wholly-owned subsidiary
of the Manager, and their affiliates (collectively "Dreyfus") for payments
made for Servicing, at an aggregate annual rate of up to .20 of 1% of the
value of the average daily net assets of Class A. Both the Distributor and
Dreyfus may pay Service Agents (a securities dealer, financial institution or
other industry professional) a fee in respect of Class A shares owned by
shareholders with whom the Service Agent has a Servicing relationship or for
whom the Service Agent is the dealer or holder of record. Both the
Distributor and Dreyfus determine the amounts to be paid to Service Agents to
which it will make payments and the basis on which such payments are made.
During the year ended January 31, 1996, $1,246,201 was charged to the Fund
pursuant to the Plan.
    Under the Distribution Plan with respect to Class B shares ("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 Class B shares at an aggregate annual rate of up to .20 of 1% of
the value of the average daily net assets of Class B. For the period March
31, 1995 through January 31, 1996, $22,866 was charged to the Fund pursuant
to the Class B Distribution Plan.
    (C) Under the Fund's Shareholder Services Plan with respect to Class A
("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus Service
Corporation 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
GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
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 year ended
January 31, 1996, the Fund was charged an aggregate of $381,305 pursuant to
the Class A Shareholder Services Plan, of which $69,755 was reimbursed by the
Manager.
    Under the Fund's Shareholder Services Plan with respect to Class B
("Class B Shareholder Services Plan"), effective March 31, 1995, the Fund
pays the Distributor for the provision of certain services to the holders of
Class B shares a fee at an annual rate of .25 of 1% of the value of the
average daily net assets of Class B. The services provided may include
personal services relating to shareholder accounts, such as answering
shareholder inquiries regarding the Fund and providing reports and other
information, and services related to the maintenance of shareholder accounts.
The Distributor may make payments to Service Agents in respect of these
services.  The Distributor determines the amounts to be paid to Service Agents.
    The Manager has undertaken, through January 31, 1997, that if the
aggregate expenses of Class B of the Fund (excluding certain expenses as
described above) exceed 1% of the value of the average daily net assets of
Class B, the Manager will reimburse the expenses of the Fund under the Class
B Shareholder Services Plan to the extent of any excess expense and up to the
full fee payable under the Class B Shareholder Services Plan. For the period
March 31, 1995 through January 31, 1996, $28,582 was charged to the Fund
pursuant to the Class B Shareholder Services Plan, of which $7,655 was
reimbursed by the Manager.
    (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 MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL MONEY MARKET FUND, INC.
    We have audited the accompanying statement of assets and liabilities of
General Money Market Fund, Inc., including the statement of investments, as
of January 31, 1996, and the related statement of operations for the year
then ended, the statement of changes in net assets for each of the two years
in the period then ended, and financial highlights for each of the years
indicated therein. These financial statements and financial highlights are
the responsibility of the Fund's management. Our responsibility is to express
an opinion on these financial statements and financial highlights based on
our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements. Our procedures included confirmation of
securities owned as of January 31, 1996 by correspondence with the custodians
and brokers. An audit also includes assessing the accounting principles used
and significant estimates made by management, as well as evaluating the
overall financial statement presentation. We believe that our audits provide
a reasonable basis for our opinion.
    In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the financial
position of General Money Market Fund, Inc. at January 31, 1996, the results
of its operations for the year then ended, the changes in its net assets for
each of the two years in the period then ended, and the financial highlights
for each of the indicated years, in conformity with generally accepted
accounting principles.
                              [Ernst & Young signature logo]

New York, New York
March 6, 1996
GENERAL 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
DREYFUS TRANSFER, INC.
ONE AMERICAN EXPRESS PLAZA
PROVIDENCE, RI 02903






FURTHER INFORMATION IS CONTAINED
IN THE PROSPECTUS, WHICH MUST
PRECEDE OR ACCOMPANY THIS REPORT.



PRINTED IN U.S.A.                          196/696AR961

GENERAL
MONEY MARKET
FUND, INC.
[G logo]





ANNUAL REPORT
January 31, 1996



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