GENERAL MONEY MARKET FUND INC
N-30D, 1999-08-06
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General Money
Market Fund, Inc.

SEMIANNUAL REPORT
May 31, 1999

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

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

Year 2000 Issues (Unaudited)

The fund could be adversely affected if the computer systems used by The Dreyfus
Corporation and the fund's other service providers do not properly process and
calculate date-related information from and after January 1, 2000. The Dreyfus
Corporation is working to avoid Year 2000-related problems in its systems and to
obtain assurances from other service providers that they are taking similar
steps. In addition, issuers of securities in which the fund invests may be
adversely affected by Year 2000-related problems. This could have an impact on
the value of the fund's investments and its share price.

<PAGE>

                                   Contents

                                   THE FUND

- -------------------------------------------

                              2     Letter from the President

                              3     Discussion of Fund Performance

                              6     Statement of Investments

                             10     Statement of Assets and Liabilities

                             11     Statement of Operations

                             12     Statement of Changes in Net Assets

                             13     Financial Highlights

                             15     Notes to Financial Statements

                                    FOR MORE INFORMATION

- --------------------------------------------------------

                                    Back Cover

<PAGE>

    General Money
Market Fund, Inc.        The Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

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

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

Despite lower nominal interest rates for most money market funds, very low
inflation continued to support above-average real returns, which are nominal
yields less the rate of inflation.

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

Sincerely,

/s/ Stephen E. Canter

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

2

<PAGE>
DISCUSSION OF FUND PERFORMANCE

Patricia A. Larkin, Senior Portfolio Manager

How did General Money Market Fund, Inc.
perform during the period?

For the six-month period ended May 31, 1999, General Money Market Fund, Inc.
produced an annualized yield of 4.34% for Class A shares and 4.14% for Class B
shares which, taking into account the effect of compounding, created an
annualized effective yield of 4.43% for Class A shares and 4.22% for Class B
shares.(1) For the six months ended May 31, 1999, the fund provided a total
return of 2.18% for Class A shares and 2.08% for Class B shares(2) compared to
the Lipper Money Market Instrument Funds category average total return of
2.13%( 3) for the  same period.

We attribute the fund's yield to the fact that the fund's average maturity was
extended, which enabled it to lock in higher returns in an environment
characterized, for all but the end of the period, by declining interest rates.

What is the fund's investment approach?

There are many factors we consider when managing General Money Market Fund, Inc.
We closely monitor the outlook for growth and inflation. We also follow overseas
developments for any influence they may have on the domestic economy. The
posture of the Federal Reserve Board is also a key determinant in our decision
as how to best structure the portfolio.

We actively manage the average maturity of the fund in an effort to take
advantage of expected changes in interest rates based upon our economic outlook.
For example, if we believe that interest rates will fall, we typically will
lengthen our average maturity in order to lock in today's higher rates.
Conversely, in a rising rate environment, we will shorten our maturities in
order to be able to reinvest at higher rates in the future.

                                                                      The Fund 3

<PAGE>
DISCUSSION OF FUND PERFORMANCE (continued)

The fund will buy only securities that are rated in one of the two highest
rating categories or are of comparable credit quality according to Dreyfus
credit analysts. This policy permits the fund to provide competitive returns
while ensuring that there is sufficient liquidity to meet our clients' needs.

What other factors influenced the fund's performance?

Last fall, the Open Market Committee of the Federal Reserve Board cut short-term
interest rates three times in an attempt to provide liquidity and improve
investor confidence in the wake of global market turmoil. From that time and
through the end of the reporting period, despite some concern that the economy
might show signs of growing too quickly, the Fed had held interest rates steady.
The relatively longer average maturity of our fund benefited from stable rates
and the Fed's accommodative stance.

What is the fund's current strategy?

Since last year's global financial crisis, the overseas environment has
stabilized and the global markets have continued to strengthen. The U.S.
financial markets have redirected their attention to the domestic economy by
focusing on the pace of economic growth and on the future outlook for
inflation. During most of the reporting period, the domestic economy enjoyed a
period of accelerating growth within a non-inflationary environment.
Statistical data  continued to show strength within many areas of the economy
including labor, housing, and a recovering manufacturing sector. However, a key
piece of inflation data eventually emerged which suggested the pick up in
inflation.

4

<PAGE>
This important factor in combination with the shift to an asymmetrical bias by
the Federal Open Market Committee (FOMC) at its May meeting, raised concerns
that the FOMC will take pre-emptive action to head off any serious threat of
inflation. The FOMC meets at the end of June and we are carefully monitoring
market conditions while continuing to seek buying opportunities.

June 14, 1999

[FN]
1. Annualized effective yield is based upon dividends declared daily and
   reinvested monthly. Past performance is no guarantee of future results.
   Yields fluctuate.

2. Total return includes reinvestment of dividends. An investment in the fund
   is not insured or guaranteed by the FDIC or any other government agency.
   Although the fund seeks to preserve the value of your investment at
   $1.00 per share, it is possible to lose money by investing in the fund.

3. Source: Lipper Analytical Services, Inc.
</FN>
                                                                      The Fund 5

<PAGE>
STATEMENT OF INVESTMENTS
May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------
                                                     Principal
Negotiable Bank Certificates of Deposit--39.7%      Amount ($)       Value ($)
- --------------------------------------------------------------------------------
Abbey National PLC (Yankee)
  5.20%, 12/9/1999                                  50,000,000      50,000,000
ABN-AMRO Bank Chicago (Yankee)
  4.94%, 4/24/2000 (a)                             100,000,000      99,947,440
Bank Austria AG (Yankee)
  5.42%, 5/22/2000                                  50,000,000      49,974,229
Barclays Bank PLC (Yankee)
  4.94%, 4/10/2000 (a)                              50,000,000      49,978,610
Canadian Imperial Bank of Commerce (Yankee)
  5.03%, 1/27/2000                                  50,000,000      49,990,485
Commerzbank AG (Yankee)
  5.19%-5.29%, 3/1/2000-5/12/2000                  175,000,000     174,963,027
Crestar Bank (Yankee)
  5.00%, 1/19/2000 (a)                              50,000,000      50,000,000
Deutsche Bank AG  (Yankee)
  5.01%, 1/6/2000                                   50,000,000      49,997,105
Deutsche Bank AG (Yankee)
  4.95%, 4/10/2000 (a)                             125,000,000     124,952,793
Generale Bank (Yankee)
  5.00%, 11/17/1999                                 50,000,000      49,993,298
Istituto Bancario San Paolo Di Torino (Yankee)
  5.15%-5.75%, 7/20/1999-5/16/2000                 180,000,000     179,969,967
Michigan National Bank (Yankee)
  4.92%, 9/10/1999                                  24,000,000      24,000,589
Royal Bank of Canada (Yankee)
  4.94%, 4/27/2000-5/4/2000 (a)                    100,000,000      99,954,304
Skandinaviska Enskilda Banken (Yankee)
  4.88%, 6/4/1999 (a)                              100,000,000     100,000,000
Societe Generale (Yankee)
  5.03%-5.25%, 1/14/2000-3/15/2000                 110,000,000     109,961,098
Svenska Handelsbanken NY (Yankee)
  5.14%, 3/20/2000                                  50,000,000      49,992,296
SwedBank (Yankee)
  5.29%, 7/12/1999                                  15,000,000      15,004,994
Toronto Dominion Bank (Yankee)
  5.14%, 2/22/2000                                  25,000,000      24,993,855
Toronto Dominion Bank (Yankee)
  4.94%, 4/10/2000 (a)                              50,000,000      49,977,960
Total Negotiable Bank Certificates of Deposit
  (cost $1,403,652,050)                                          1,403,652,050

6

<PAGE>
- --------------------------------------------------------------------------------
                                                     Principal
Commercial Paper--26.5%                             Amount ($)       Value ($)
- --------------------------------------------------------------------------------
DaimlerChrysler North America Holding Corp.
  4.92%, 7/16/1999                                  50,000,000      49,696,875
Den Norske Bank ASA
  4.96%, 10/26/1999                                 74,000,000      72,539,024
Fina Oil & Chemical Co.
  4.95%-4.99%, 6/7/1999-6/15/1999(b,c)              27,244,000      27,213,381
FINOVA Capital Corp.
  5.03%-5.04%, 6/11/1999-9/22/1999                  95,000,000      93,746,378
Ford Motor Credit Corp.
  4.92%, 6/1/1999                                   75,000,000      75,000,000
General Electric Capital Corp.
  5.37%, 6/4/1999                                   25,000,000      24,989,250
HSBC Americas Inc.
  5.12%, 9/2/1999                                   45,000,000      44,427,120
Heller Financial Inc.
  5.01%, 7/9/1999                                   25,000,000      24,869,639
Hertz Corp.
  4.90%, 7/9/1999                                   50,000,000      49,742,972
Lehman Brothers Holdings Inc.
  5.40%-5.42%, 8/5/1999-8/19/1999                  150,000,000     148,370,861
Paine Webber Group Inc.
  5.08%, 9/20/1999                                  10,000,000       9,847,375
Spintab AB
  4.97%-5.09%, 6/22/1999-10/4/1999                 175,000,000     173,407,997
SwedBank Inc.
  4.96%, 10/20/1999                                 75,000,000      73,578,250
UBS Finance (DE) Inc.
  4.85%, 6/1/1999                                   70,000,000      70,000,000
Total Commercial Paper
  (cost $937,429,122)                                              937,429,122
- --------------------------------------------------------------------------------

Bank Notes--12.6%
- --------------------------------------------------------------------------------
Abbey National PLC
  5.37%, 6/1/1999                                   35,000,000      35,000,000
Comerica Bank
  4.94%, 3/22/2000 (a)                              50,000,000      49,984,783
First Tennessee Bank
  4.93%, 4/19/2000 (a)                              75,000,000      74,974,047
First Union National Bank
  5.21%, 9/24/1999                                  50,000,000      50,000,000

                                                                      The Fund 7


<PAGE>
STATEMENT OF INVESTMENTS  (Unaudited) (continued)

- --------------------------------------------------------------------------------
                                                     Principal
Bank Notes (continued)                              Amount ($)       Value ($)
- --------------------------------------------------------------------------------
LaSalle National Bank
  5.15%, 2/22/2000                                  25,000,000      24,993,859
NationsBank N.A.
  5.00%, 1/5/2000                                   10,000,000      10,000,000
NationsBank N.A.
  4.87%, 8/3/1999-8/6/1999 (a)                     100,000,000      99,993,108
Old Kent Bank & Trust Co.
  4.95%, 5/3/2000 (a)                              100,000,000      99,955,804
Total Bank Notes
  (cost $444,901,601)                                              444,901,601
- --------------------------------------------------------------------------------

Corporate Notes-11.1%
- --------------------------------------------------------------------------------
CIT Group Holdings Inc.
  4.88%-4.97%, 9/29/1999-11/2/1999 (a)              75,000,000      74,990,932
Ford Motor Credit Corp.
  4.95%, 5/5/2000 (a)                               60,000,000      60,000,000
Heller Financial Inc.
  5.00%-5.01%, 9/8/1999-3/21/2000 (a)               20,000,000      20,004,193
IBM Credit Corp.
  4.85%, 6/18/1999 (a)                              50,000,000      49,998,636
Merrill Lynch & Co. Inc.
  4.92%, 10/13/1999 (a)                             25,000,000      25,000,000
Paine Webber Group Inc.
  5.02%-5.12%, 7/29/1999-4/20/2000 (a)             113,000,000     113,004,018
Salomon Smith Barney Holdings Inc.
  5.00%, 10/28/1999 (a)                             50,000,000      50,000,000
Total Corporate Notes
  (cost $392,997,779)                                              392,997,779
- --------------------------------------------------------------------------------

Promissory Notes-4.9%
- --------------------------------------------------------------------------------
Goldman Sachs Group L.P.
  5.00%-5.11%, 7/16/1999-9/8/1999 (b,c)
    (cost $175,000,000)                            175,000,000     175,000,000
- --------------------------------------------------------------------------------

U.S. Treasury Bills-.7%
- --------------------------------------------------------------------------------
  4.35%, 1/6/2000
  (cost $24,365,813)                                25,000,000      24,365,813

8

<PAGE>
- --------------------------------------------------------------------------------
                                                     Principal
U.S. Government Agencies--1.4%                      Amount ($)       Value ($)
- --------------------------------------------------------------------------------
Federal National Mortgage Association, Floating
  Rate Notes
  4.83%, 12/1/1999 (a)
  (cost $50,000,000)                                50,000,000      50,000,000

- --------------------------------------------------------------------------------

Time Deposits--2.4%
- --------------------------------------------------------------------------------
Berliner Handels-und Frankforter Bank AG
  (Grand Cayman)
  4.50%, 6/1/1999                                   53,376,000      53,376,000
Westdeutsche Landesbank Girozentrale
  (Grand Cayman)
  4.81%, 6/1/1999                                   30,000,000      30,000,000
Total Time Deposits
  (cost $83,376,000)                                                83,376,000
- --------------------------------------------------------------------------------

Total Investments (cost $3,511,722,365)                  99.3%   3,511,722,365

Cash and Receivables (Net)                                 .7%      26,892,624

Net Assets                                              100.0%   3,538,614,989
[FN]
a. Variable interest rate--subject to periodic change.

b. These notes were acquired for investment, not with intent to distribute or
   sell.

c. Securities restricted as to public resale. These securities were acquired
   from 10/19/1998-5/11/1999 at a cost of par value. At May 31, 1999, the
   aggregate value of these securities is $202.2 million representing
   approximately 5.7% of net assets and are valued at amortized cost.
</FN>

See notes to financial statements.

                                                                      The Fund 9


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

- --------------------------------------------------------------------------------

                                                         Cost            Value
- --------------------------------------------------------------------------------
Assets ($):
Investments in securities--See Statement of
  Investments                                    3,511,722365    3,511,722,365
Interest receivable                                                 34,331,311
Prepaid expenses                                                       173,467
                                                                 3,546,227,143
- --------------------------------------------------------------------------------
Liabilities ($):
Due to The Dreyfus Corporation and affiliates                        2,449,964
Due to Distributor                                                     367,002
Cash overdraft due to Custodian                                      4,546,252
Accrued expenses                                                       248,936
                                                                     7,612,154
- --------------------------------------------------------------------------------
Net Assets ($)                                                   3,538,614,989
- --------------------------------------------------------------------------------
Composition of Net Assets ($):
Paid-in capital                                                  3,538,694,840
Accumulated net realized gain (loss) on investments                    (79,851)
- --------------------------------------------------------------------------------
Net Assets ($)                                                   3,538,614,989
- --------------------------------------------------------------------------------


- --------------------------------------------------------------------------------
Net Asset Value Per Share

                                                      Class A          Class B
- --------------------------------------------------------------------------------
Net Assets ($)                                    859,159,275    2,679,455,714
Shares Outstanding                                859,212,657    2,679,482,183
- --------------------------------------------------------------------------------
Net Asset Value Per Share                                 1.00            1.00


See notes to financial statements.

10
<PAGE>
STATEMENT OF OPERATIONS
Six Months Ended May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------

Investment Income ($)
- --------------------------------------------------------------------------------
Interest Income                                                  89,129,894
Expenses:
Management fee--Note 2(a)                                         8,678,650
Shareholder servicing costs--Note 2(c)                            4,319,057
Distribution fees--Note 2(b)                                      3,471,460
Registration fees                                                   250,943
Custodian fees                                                       91,068
Professional fees                                                    31,406
Prospectus and shareholders' reports                                 30,918
Directors' fees and expenses--Note 2(d)                              19,185
Miscellaneous                                                         7,885
Total Expenses                                                   16,900,572
Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                           (485,223)
Net Expenses                                                     16,415,349
Investment Income--Net                                           72,714,545
- --------------------------------------------------------------------------------
Realized Gain (Loss) on Investments--Note 1(b) ($)                  (11,401)
Net Increase in Net Assets Resulting from Operations             72,703,144

See notes to financial statements.

                                                                     The Fund 11

<PAGE>
STATEMENT OF CHANGES IN NET ASSETS

- --------------------------------------------------------------------------------
                                        Six Months Ended
                                            May 31, 1999             Year Ended
                                             (Unaudited)      November 30, 1998
- --------------------------------------------------------------------------------
Operations ($):
Investment income--net                        72,714,545            125,073,830
Net realized gain (loss) on investments          (11,401)                36,653
Net Increase (Decrease) in Net Assets
  Resulting from Operations                   72,703,144            125,110,483
- --------------------------------------------------------------------------------
Dividends to Shareholders from ($):
Investment income--net:
Class A shares                               (18,588,587)           (42,077,699)
Class B shares                               (54,125,958)           (82,996,131)
Total Dividends                              (72,714,545)          (125,073,830)
- --------------------------------------------------------------------------------
Capital Stock Transactions ($):
Net proceeds from shares sold:
Class A shares                             3,026,714,111          5,634,804,053
Class B shares                             4,089,701,849          6,698,310,567
Dividends reinvested:
Class A shares                                18,259,678             41,121,880
Class B shares                                52,764,846             80,819,334
Cost of shares redeemed:
Class A shares                            (3,021,517,829)        (5,743,540,176)
Class B shares                            (3,890,334,509)        (5,582,959,197)
Increase (Decrease) in Net Assets from
  Capital Stock Transactions                 275,588,146          1,128,556,461
Total Increase (Decrease) in Net Assets      275,576,745          1,128,593,114
- --------------------------------------------------------------------------------
Net Assets ($):
Beginning of Period                        3,263,038,244          2,134,445,130
End of Period                              3,538,614,989          3,263,038,244

See notes to financial statements.

12

<PAGE>

FINANCIAL HIGHLIGHTS

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

<TABLE>
<CAPTION>

- --------------------------------------------------------------------------------------------------------------------------------
                                       Six Months                         Ten Months
                                            Ended        Year Ended            Ended
                                     May 31, 1999      November 30,      November 30,             Year Ended January 31,
                                                                                           -------------------------------------
Class A Shares                        (Unaudited)              1998            1997(a)        1997     1996     1995     1994
- --------------------------------------------------------------------------------------------------------------------------------
<S>                                      <C>                <C>              <C>           <C>      <C>      <C>      <C>
Per Share Data ($):
Net asset value, beginning
  of period                                 1.00               1.00             1.00          1.00     1.00     1.00     1.00
Investment Operations:
Investment income--net                      .022               .049             .041          .047     .053     .037     .025
Distributions:
Dividends from investment
  income--net                              (.022)             (.049)           (.041)        (.047)   (.053)   (.037)   (.025)
Net asset value, end of period              1.00               1.00             1.00          1.00     1.00     1.00     1.00
- --------------------------------------------------------------------------------------------------------------------------------
Total Return (%)                            4.37(b)            4.98             4.99(b)       4.81     5.42     3.75     2.56
- --------------------------------------------------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average
  net assets                                 .79(b)             .77              .88(b)        .84      .86      .94      .94
Ratio of net investment income
  to average net assets                     4.34(b)            4.88             4.89(b)       4.71     5.28     3.68     2.53
Decrease reflected in above
  expense ratios due to
  undertakings by the Manager                 --                 --               --            --      .01      .04      .02
Net Assets, end of period
  ($ x 1,000's)                          859,159            835,706          903,313       764,119  654,581  572,116  616,072

<FN>
a The fund changed its fiscal year end from January 31 to November 30.
b Annualized.
See notes to financial statements.
</FN>
</TABLE>
                                                                     The Fund 13

<PAGE>

<TABLE>
<CAPTION>
- ----------------------------------------------------------------------------------------------------------------------
                                          Six Months                      Four Months
                                               Ended       Year Ended           Ended
                                        May 31, 1999     November 30,    November 30,        Year Ended January 31,
                                                                                          ----------------------------
Class B Shares                           (Unaudited)             1998           1997(a)       1997         1996b
- ----------------------------------------------------------------------------------------------------------------------
<S>                                        <C>              <C>             <C>            <C>            <C>
Per Share Data ($):
Net asset value, beginning of period            1.00             1.00            1.00         1.00          1.00
Investment Operations:
Investment income--net                          .021             .047            .039         .046          .043
Distributions:
Dividends from investment income--net          (.021)           (.047)          (.039)       (.046)        (.043)
Net asset value, end of period                  1.00             1.00            1.00         1.00          1.00
- ----------------------------------------------------------------------------------------------------------------------
Total Return (%):                               4.17(c)          4.78            4.83(c)      4.65           518(c)
- ----------------------------------------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average net assets         1.00(c)          1.00            1.00(c)      1.00          1.00(c)
Ratio of net investment income
  to average net assets                         4.14(c)          4.66            4.78(c)      4.56          5.00(c)
Decrease reflected in above expense ratios
  due to undertakings by the Manager             .04(c)           .06             .05(c)       .07           .07(c)
Net Assets, end of period ($ x 1,000)      2,679,456        2,427,332       1,231,132      369,205        50,446

<FN>
a The fund changed its fiscal year end from January 31 to November 30.
b From March 31, 1995 (Commencement of initial offering) to January 31, 1996.
c Annualized.
See notes to financial statements.

</FN>
</TABLE>

14

<PAGE>
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, as amended (the "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 (the "Manager") serves as the
fund's investment adviser. The Manager is a direct subsidiary of Mellon Bank,
N.A.

Premier Mutual Fund Services, Inc. (the "Distributor") is the distributor of the
fund's shares, which are sold to the public without a sales load. The fund is
authorized to issue 25 billion shares of $.01 par value Common Stock. The fund
currently offers two classes of shares: Class A (15 billion shares authorized)
and Class B (10 billion shares authorized). 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 (a securities dealer financial institution or other industry
professional) at an annual rate of .05% of the value of the average daily net
assets of Class B shares.

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

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

                                                                     The Fund 15

<PAGE>

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

(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.
Under the terms of the custody agreement, the fund received net earnings credits
of $711 during the period ended May 31, 1999 based on available cash balances
left on deposit. Income earned under this arrangement is included in interest
income.

The fund may enter into repurchase agreements with financial institutions,
deemed to be creditworthy by the fund's Manager, subject to the seller's
agreement to repurchase and the fund's agreement to resell such securities at a
mutually agreed upon price. Securities purchased subject to repurchase
agreements are deposited with the fund's custodian and, pursuant to the terms of
the repurchase agreement, must have an aggregate market value greater than or
equal to the repurchase price plus accrued interest at all times. If the value
of the underlying securities falls below the value of the repurchase price plus
accrued interest, the fund will require the seller to deposit additional
collateral by the next business day. If the request for additional collateral is
not met, or the seller defaults on its repurchase obligation, the fund maintains
the right to sell the underlying securities at market value and may claim any
resulting loss against the seller.

(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, if any, are normally declared
and paid annually, but the fund may make distributions on a more frequent basis
to comply with the distribution requirements of the Internal Revenue Code of
1986, as amended (the "Code"). To the extent that net realized capital gain can
be offset by capital loss carryovers, it is the policy of the fund not to
distribute such gain.

16

<PAGE>
(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 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 $69,000 available
for Federal income tax purposes to be applied against future net securities
profits, if any, realized subsequent to November 30, 1998. If not applied, the
carryover expires in fiscal 2005.

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

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

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

(b) Under the Service Plan with respect to Class A shares (the "Plan"), adopted
pursuant to Rule 12b-1 under the Act, Class A shares directly bear the cost of
preparing, printing and distributing prospectuses and statements of additional
information and implementing and operating the Plan. In addition, Class A
shares reimburse (a) the Distributor for payments made for distributing Class A
shares and servicing shareholder accounts ("Servicing") and (b) the Manager,
Dreyfus Service

                                                                     The Fund 17

<PAGE>
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

Corporation, a wholly-owned subsidiary of the Manager, and their affiliate
(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 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. The schedule of such fees and the basis upon which such fees will be
paid shall be determined from time to time by the fund's Board of Directors. If
a holder of Class A shares ceases to be a client of a Service Agent, but
continues to hold Class A shares, Dreyfus will be permitted to act as a Service
Agent in respect of such fund shareholders and receive payments under the
Service Plan for Servicing. The fees payable for Servicing are payable without
regard to actual expenses incurred. During the period ended May 31, 1999, Class
A shares were charged $856,594 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, Class B
shares directly bear 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, Class B shares reimburse
the Distributor for payments made to third parties for distributing their
shares at an aggregate annual rate of up to .20% of 1% of the value of the
average daily net assets of Class B. During the period ended May 31, 1999,
Class B shares were charged $2,614,866 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"), Class A shares reimburse 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 personal services and/or maintaining shareholder accounts. The
services provided may include personal services relating to shareholder
accounts, such as answering shareholder inquiries regarding Class A shares and
providing reports and other information, and services related to the
maintenance of

18

<PAGE>
shareholder accounts. During the period ended May 31, 1999, Class A shares
were charged $200,685 pursuant to the Class A Shareholder Services Plan.

Under the fund's Shareholder Services Plan with respect to Class B ("Class
B Shareholder Services Plan"), Class B shares pay 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 Class B shares and
providing reports and other information, and services related to the maintenance
of shareholder accounts. The Distributor may make payments to Service Agents in
respect of these services. The Distributor determines the amounts to be paid to
Service Agents.

The Manager has undertaken through May 31, 1999, that if the aggregate expenses
of Class B shares (exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses) exceed 1% of the value of the average daily net assets
of Class B, the Manager will reimburse the expenses of the fund under the Class
B Shareholder Services Plan to the extent of any excess expense and up to the
full fee payable under the Class B Shareholder Services Plan. During the period
ended May 31, 1999, $3,922,299 were charged pursuant to the Class B Shareholder
Services Plan, of which $485,223 was reimbursed by the Manager.

The fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager, under a transfer agency agreement for providing personnel and
facilities to perform transfer agency services for the fund. During the period
ended May 31, 1999, the fund was charged $105,025 pursuant to the transfer
agency agreement.

(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.

                                                                     The Fund 19

<PAGE>

NOTES

<PAGE>

For More Information

                     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, New York

                     Transfer Agent &
                     Dividend Disbursing Agent

                     Dreyfus Transfer, Inc.
                     P.O. Box 9671
                     Providence, RI 02940

                     Distributor

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


To obtain information:

By telephone
Call 1-800-645-6561

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

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

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

(c) 1999 Dreyfus Service Corporation  196/696SA995




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