GENERAL MONEY MARKET FUND INC
N-30D, 1999-02-05
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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.

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased to report the performance for General Money Market Fund, Inc.
for  the  12-month  period  ended  November  30, 1998, as shown in the following
table:

                                               YIELD          EFFECTIVE YIELD*
                                              _______           _____________

  Class A Shares . .. . . . . . .              4.88%                 4.98%

  Class B Shares . .. . . . . . .              4.68%                 4.78%

ECONOMIC REVIEW

  During  1998,  the  main  regions  of  the  world  had very different economic
fundamentals.  The  U.S.  entered  the  year  with  a  strong  economy near full
employment, with unemployment only slightly above 4%. The tight labor market led
the  Federal  Reserve Board to contemplate a rise in interest rates early in the
year.  The  U.S.  economy  cooled enough over the months that the Fed decided to
stand  pat.  Evidence  of  economic  cooling continued to accumulate and worries
about  the  world economy intensified. Financial stresses pushed the Fed to ease
beginning  in September. After many years of subpar economic growth, continental
Europe  moved  into a sustained economic expansion. The overall European economy
benefited  as  interest  rates  in  peripheral countries such as Spain and Italy
fell, approaching the lower level established by Germany, on the eve of currency
unification.  Unlike  the  U.S.,  Europe  has  substantial  excess  capacity  of
productive  plants and labor. In Asia, weak economies were pervasive as a result
of  the  Asian  financial  crisis.  The Latin American economies weakened as the
financial stresses spread throughout that region.

  A  main  influence  on  the  U.S.  economy this year was the foreign financial
crisis  and cooling of the world economy. The positive effects hit first. Actual
inflation  and  expected  inflation  dropped,  causing  a  decline  in long-term
Treasury bond yields and mortgage rates. This caused a boom in housing. The drop
in inflation helped the consumer sector as more of the growth in consumer income
was  left  over  after  inflation to buy goods and services. Consumers benefited
from a combination of good growth in real income, a strong labor market and past
increases in the prices of assets they owned.

  The  negative  effect of Asian weakness was felt in the industrial sector more
than  the  consumer  sector.  Corporate  profits weakened, especially in sectors
affected  by  the Asian crisis such as world-traded commodities (oil, metals and
paper) and exports. One result of the industrial weakness was to cool off a U.S.
economy that had been growing rapidly.

  The  major  change  in  the  economic  outlook  over  recent months has been a
downward  shift  in  expectations  for  world  economic  growth. A credit crunch
developed in emerging countries and former communist countries, sharply reducing
the   economic   outlook   for   Asia   and   Latin   America  as  well  as  for
commodity-exporting countries throughout the world. The effect on Europe and the
U.S. has been to lower expectations of profit growth and drive down bond yields.
Monetary policy has begun to ease in Europe as well as the U.S.

  Evidence  of  a  weaker  world  economy  accumulated as the financial stresses
continued.  A  worsened financial crisis occurred between the Russian default in
mid-August  and  the  fallout  from  the Long-Term Capital Management hedge fund
crisis  through  early October. However, proactive steps were taken to stabilize
the  Japanese  banks,  design  a  support  package  for Brazil and ease monetary
policy.  There  appears to be a shift in the priorities of key policymakers from
fighting potential inflation to restimulating future world economic growth.

MARKET ENVIRONMENT/PORTFOLIO FOCUS

  The  economic  forces described above drove down interest rates in late summer
and  early  fall.  While there has been a recent modest increase, rates have now
broken out of the narrow band that prevailed earlier in the year.

  The  flight  to  safety that was prompted by economic worries around the globe
generated   very  high  demand  for  U.S.  Treasury  securities  in  the  longer
maturities.  This  drove  down  yields  but  money market rates remained strong,
causing an inverted yield curve for a while.

In recent weeks, investors appeared to become more confident with the economic
outlook. The result was an unwinding of large portions of the positions taken as
a  result  of  the  search for investment safety. Consequently, the yield curve,
which  measures  the  relationship  between  long-  and  short-term  securities,
returned to a more positive or more normal pattern.

  At  present,  prices  and  rates  in  the  money market are more reflective of
underlying  economic  forces than of investor fears of global financial turmoil.
This  of  course,  is  constructive  for  investors  in  short-term money market
instruments.

The fact that the Federal Reserve Open Market Committee lowered interest rates
three times since late September has been a strong confidence-building factor in
the  markets.  Currently, the market expects the Fed to continue its bias toward
accommodation as economic conditions dictate.

  Taking  all  this  into  account,  we  continue  to maintain a somewhat longer
average  maturity than the average for other funds. This is intended to position
the Fund in the event of further downward moves in market yields.

               Sincerely,

               [Patricia A. Larkin  signature]




               Patricia A. Larkin

               Senior Portfolio Manager

December 18, 1998
New York, N.Y.

* Effective yield takes into account the effect of compounding and is based upon
dividends declared daily and reinvested monthly.

<TABLE>
GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    NOVEMBER 30, 1998

                                                                                                   Principal

Negotiable Bank Certificates of Deposit--24.2%                                                      Amount           Value
- -------------------------------------------------------                                         _____________   _______________
<S>                                                                                             <C>            <C>
Bankers Trust Co.

   6.00%, 12/10/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  50,000,000  $     50,000,118

Bank of Nova Scotia (Yankee)

   5.12%, 4/6/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         30,000,000        30,001,023

Credit Agricole Indosuez S.A. (Yankee)

   4.87%-5.12%, 4/16/99-5/26/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .         49,000,000        49,001,679

Creditanstalt-Bankverein (Yankee)

   4.86%-5.77%, 4/16/99-5/26/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .         75,000,000        74,981,418

Credit Suisse First Boston (Yankee)

   4.86%, 4/14/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        50,000,000

Deutsche Bank AG  (Yankee)

   5.61%-5.70%, 2/26/99-3/22/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,993,706

Generale Bank (Yankee)

   5.00%, 11/17/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,986,081

Istituto Bancario San Paolo Di Torino

   5.74%-5.75%, 7/20/99-7/28/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        100,000,000        99,965,360

Norddeutsche Landesbank Girozentrale (Yankee)

   5.12%, 4/6/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         30,000,000        30,044,487

Societe Generale (Yankee)

   5.77%-5.85%, 4/6/99-5/28/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         60,000,000        59,984,903

Skandinaviska Enskilda Banken (Yankee)

   4.88%, 6/4/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        100,000,000       100,000,000

SwedBank (Yankee)

   5.29%-5.73%, 3/26/99-7/12/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         55,000,000        55,021,124

Swiss Bank Corp. (Yankee)

   5.74%, 3/5/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         40,000,000        39,995,558

Westdeutsche Landesbank Girozentrale (Yankee)

   5.04%, 4/13/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        50,000,000
                                                                                                                _______________

TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT

   (cost $788,975,457) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      $   788,975,457
                                                                                                                ===============


Commercial Paper--39.0%
- -------------------------------------------------------

ABN-AMRO North America Finance Inc.

   5.00%, 4/23/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  50,000,000  $     49,026,806

Associates Corp. of North America

   5.45%, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        25,000,000

BT Alex Brown Inc.

   5.73%, 12/24/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,929,722

Bear Stearns Companies Inc.

   5.66%, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

Canadian Imperial Holdings Inc.

   4.89%, 4/26/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,032,344

Daimler-Benz North America Corp.

   4.90%-5.04%, 3/12/99-4/28/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         74,250,000        73,074,249

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                     NOVEMBER 30, 1998

                                                                                                   Principal
Commercial Paper (continued)                                                                        Amount           Value
- -------------------------------------------------------                                         _____________   _______________

Den Danske Corp. Inc.

   5.12%, 4/1/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  25,000,000  $     24,580,281

Den Norske Bank ASA

   5.12%, 5/12/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        48,877,250

FINOVA Capital Corp.

   5.70%-5.74%, 2/19/99-2/25/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        115,000,000       113,562,490

Generale Bank Inc.

   5.65%-5.66%, 12/2/98-12/7/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        100,000,000        99,946,528

General Electric Capital Corp.

   5.37%-5.66%, 3/1/99-6/4/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        150,000,000       147,415,750

HSBC Americas Inc.

   5.12%, 9/2/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         45,000,000        43,312,160

Heller Financial Inc.

   5.40%-5.76%, 12/16/98-4/5/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         85,000,000        84,401,667

Hertz Corp.

   5.64%, 12/11/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,923,194

Lehman Brothers Holdings Inc.

   4.91%-5.78%, 2/1/99-2/8/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .         35,000,000        34,809,178

Merrill Lynch & Co. Inc.

   5.66%-5.71%, 1/19/99-3/26/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         95,000,000        93,992,009

Morgan (J.P.) Co. Inc.

   5.63%, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        50,000,000

Spintab AB

   5.09%-5.70%, 12/15/98-6/30/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        145,000,000       143,629,782

SwedBank Inc.

   5.10%-5.54%, 2/5/99-5/17/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        105,000,000       103,323,821
                                                                                                                _______________

TOTAL COMMERCIAL PAPER

   (cost $1,273,837,231) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       $1,273,837,231
                                                                                                                 ==============


Bank Notes--13.6%
- -------------------------------------------------------

Abbey National PLC

   5.37%, 6/1/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  35,000,000  $     35,032,333

BankBoston, N.A.

   4.96%, 12/10/98 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

First Union National Bank

   4.83%-5.21%, 4/30/99-9/24/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .        150,000,000       150,004,014

NationsBank N.A.

   4.87%, 8/3/99-8/6/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        100,000,000        99,973,662

PNC Bank N.A.

   4.85%-4.87%,  4/28/99-5/21/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . .        120,000,000       119,973,873

Societe Generale

   4.88%, 2/23/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,998,205
                                                                                                                _______________

TOTAL BANK NOTES

   (cost $444,982,087) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      $   444,982,087
                                                                                                                ===============

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998

                                                                                                  Principal
Corporate Notes--15.2%                                                                              Amount            Value
- -------------------------------------------------------                                         _____________    _______________

BankBoston, N.A.

   4.91%, 1/11/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $   10,000,000  $       9,999,568

Bankers Trust Co.

   4.87%, 4/9/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         65,000,000        64,991,126

CIT Group Holdings Inc.

   4.88%-4.97%, 9/29/99-11/2/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .         75,000,000        74,978,576

Heller Financial Inc.

   5.00%-5.05%, 4/13/99-9/8/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . .         40,000,000        40,000,000

IBM Credit Corp.

   4.85%, 6/18/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,984,034

Key Bank N.A.

   4.86%, 4/16/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         45,000,000        44,990,107

Lehman Brothers Holdings Inc.

   5.05%, 1/13/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

Merrill Lynch & Co. Inc.

   4.92%, 10/13/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        25,000,000

NationsBank N.A.

   4.86%, 4/27/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        49,994,160

Paine Webber Group Inc.

   4.95%-5.52%, 1/4/99-7/29/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . .         65,000,000        65,016,625

Salomon Smith Barney Holdings Inc.

   5.00%, 10/28/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        50,000,000
                                                                                                                _______________

TOTAL CORPORATE NOTES

   (cost $494,954,196) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      $   494,954,196
                                                                                                                ===============


Promissory Notes--4.8%
- -------------------------------------------------------

Goldman Sachs Group L.P.

  4.95%-5.25%, 2/8/99-8/6/99 (b,c)

   (cost $155,000,000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $ 155,000,000   $   155,000,000
                                                                                                                ===============

U.S. Government Agencies--1.5%
- -------------------------------------------------------

Federal National Mortgage Association, Floating Rate Notes

  4.83%, 12/1/99 (a)

   (cost $50,000,000)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $   50,000,000  $     50,000,000
                                                                                                               ================

Repurchase Agreements--.3%
- -------------------------------------------------------

Goldman Sachs Group L.P.

  dated 11/30/98, due 12/1/98 in the amount of $11,001,589

  (fully collateralized by $11,075,000 U.S. Treasury Notes

  5.875%, due 3/31/99, value $11,232,492)

   (cost $11,000,000)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $   11,000,000  $     11,000,000
                                                                                                               ================

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998

                                                                                                 Principal
Time Deposits--1.9%                                                                                Amount           Value
- -------------------------------------------------------                                         _____________   _______________

Berliner Handels-und Frankforter Bank AG (Grand Cayman)

   5.19%, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $   11,908,000  $     11,908,000

Westdeutsche Landesbank Girozentrale (Grand Cayman)

   5.50%, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         50,000,000        50,000,000
                                                                                                                _______________

TOTAL TIME DEPOSITS

   (cost $61,908,000)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                     $     61,908,000
                                                                                                               ================


TOTAL INVESTMENTS

   (cost $3,280,656,971) . . . . . . . . . . . . . . . . . . . . . . . . . . . .     100.5%                      $3,280,656,971
                                                                                   _______                       ==============


LIABILITIES, LESS CASH AND RECEIVABLES . . . . . . . . . . . . . . . . . . . . .      (.5%)                   $    (17,618,727)
                                                                                   _______                      _______________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     100.0%                      $3,263,038,244
                                                                                   _______                      ===============

Notes to Statement of Investments:
- -----------------------------------------------------------------------------

(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 10/8/98 to 11/10/98 at a cost of par value. At November 30, 1998, the
    aggregate value of these securities was $155 million representing
    approximately 4.8% of the Fund's net assets and are valued at amortized
    cost.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                         NOVEMBER 30, 1998

                                                                                                    Cost             Value
                                                                                              _______________  _______________
<S>                                                                                         <C>                  <C>
ASSETS:                          Investments in securities--See Statement of
                                   Investments--Note 1(b)  . . . . . . . . . . . . . . . .  $3,280,656,971       $3,280,656,971

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                            1,868,806

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                           28,034,479

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                              161,153
                                                                                                                _______________

                                                                                                                  3,310,721,409
                                                                                                                _______________


LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                            1,183,991

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                              333,896

                                 Payable for investment securities purchased . . . . . . .                           43,312,160

                                 Payable for shares of Common Stock redeemed . . . . . . .                            2,199,024

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                              654,094
                                                                                                                _______________

                                                                                                                     47,683,165
                                                                                                                _______________


NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       $3,263,038,244
                                                                                                                _______________



REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                       $3,263,106,694

                                 Accumulated net realized gain (loss) on investments . . .                             (68,450)
                                                                                                                _______________


 NET ASSETS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       $3,263,038,244
                                                                                                                 ==============

                                                 NET ASSET VALUE PER SHARE
                                            --------------------------------------

                                                                                               Class A             Class B
                                                                                            ________________    _______________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  $    835,706,104     $2,427,332,140

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       835,756,697      2,427,349,997


 NET ASSET VALUE PER SHARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             $1.00              $1.00
                                                                                                       =====              =====


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                          YEAR ENDED NOVEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                       <C>                    <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                               $149,571,462

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . .        $  13,222,636

                                 Shareholder servicing costs--Note 2(c)  . . . . .            6,047,538

                                 Distribution fees--Note 2(b)  . . . . . . . . . .            5,289,054

                                 Registration fees . . . . . . . . . . . . . . . .              603,609

                                 Custodian fees  . . . . . . . . . . . . . . . . .              163,132

                                 Prospectus and shareholders' reports  . . . . . .              103,576

                                 Professional fees . . . . . . . . . . . . . . . .               52,028

                                 Director's fees and expenses--Note 2(d) . . . . .               38,365

                                 Miscellaneous . . . . . . . . . . . . . . . . . .               23,907

                                                                                         ______________

                                        Total Expenses . . . . . . . . . . . . . .           25,543,845


                                 Less--reduction in shareholder servicing costs due to
                                    undertaking--Note 2(c) . . . . . . . . . . . .           (1,046,213)

                                                                                         ______________


                                        Net Expenses . . . . . . . . . . . . . . .                                 24,497,632
                                                                                                                _____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                125,073,830

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . .                                     36,653
                                                                                                                _____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . .                               $125,110,483
                                                                                                                 ============













                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                    Year Ended         Ten Months Ended        Year Ended
                                                                 November 30, 1998    November 30, 1997*    January 31, 1997
                                                               ___________________     ____________________  ________________
<S>                                                               <C>                 <C>
OPERATIONS:

   Investment income--net  . . . . . . . . . . . . . . . . . .    $   125,073,830     $     68,525,556      $     49,280,474

   Net realized gain (loss) on investments . . . . . . . . . .             36,653              (78,341)               (8,067)

                                                                 ________________      ________________       _________________

          Net Increase (Decrease) in Net Assets Resulting

             from Operations . . . . . . . . . . . . . . . . .        125,110,483           68,447,215            49,272,407

                                                                 ________________     ________________      ________________



DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net:

       Class A Shares  . . . . . . . . . . . . . . . . . . . .        (42,077,699)         (32,426,980)          (34,241,653)

       Class B Shares  . . . . . . . . . . . . . . . . . . . .        (82,996,131)         (36,098,576)          (15,038,821)

                                                                 ________________     ________________      ________________

          Total Dividends  . . . . . . . . . . . . . . . . . .       (125,073,830)         (68,525,556)          (49,280,474)

                                                                 ________________     ________________      ________________



CAPITAL STOCK TRANSACTIONS ($1.00 per share):

   Net proceeds from shares sold:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .      5,634,804,053        5,481,588,637         6,572,669,153

       Class B Shares  . . . . . . . . . . . . . . . . . . . .      6,698,310,567        3,353,368,498         1,019,289,506

   Dividends reinvested:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .         41,121,880           31,506,536            32,898,001

       Class B Shares  . . . . . . . . . . . . . . . . . . . .         80,819,334           35,189,462            14,154,018

   Cost of shares redeemed:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .     (5,743,540,176)      (5,373,865,859)       (6,496,025,709)

       Class B Shares  . . . . . . . . . . . . . . . . . . . .     (5,582,959,197)      (2,526,588,101)         (714,679,626)

                                                                 ________________     ________________      ________________

          Increase (Decrease) in Net Assets from
             Capital Stock Transactions  . . . . . . . . . . .      1,128,556,461        1,001,199,173           428,305,343

                                                                 ________________     ________________      ________________


             Total Increase (Decrease) in Net Assets . . . . .      1,128,593,114        1,001,120,832           428,297,276



NET ASSETS:

   Beginning of Period . . . . . . . . . . . . . . . . . . . .      2,134,445,130        1,133,324,298           705,027,022
                                                                 ________________     ________________      ________________

   End of Period . . . . . . . . . . . . . . . . . . . . . . .     $3,263,038,244       $2,134,445,130        $1,133,324,298
                                                                   ==============       ==============        ==============

*   The Fund changed its fiscal year end from January 31 to November 30.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
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 period indicated. This information has been
derived from the Fund's financial statements.


                                                                              Class A Shares

                                                ________________________________________________________________________

                                               Year Ended       Ten Months Ended

                                               November 30,        November 30,                 Year Ended January 31,

                                                                                          __________________________________

PER SHARE DATA:                                    1998               1997(1)             1997      1996      1995      1994
                                            _____________     ________________         ______     ______    ______    ______
<S>                                            <C>                 <C>                <C>       <C>       <C>        <C>
   Net asset value, beginning of period  . .   $  1.00             $  1.00            $  1.00   $  1.00   $  1.00    $  1.00
                                                ______              ______             ______    ______    ______     ______

   Investment Operations:

   Investment income--net  . . . . . . . . .      .049                .041               .047      .053      .037      .025
                                                ______              ______             ______    ______    ______     ______

   Distributions:

   Dividends from investment income--net . .     (.049)              (.041)             (.047)    (.053)    (.037)     (.025)
                                                ______              ______             ______    ______    ______     ______

   Net asset value, end of period  . . . . .   $  1.00             $  1.00            $  1.00   $  1.00  $  1.00     $  1.00
                                               =======             =======            =======   =======  =======     =======


TOTAL INVESTMENT RETURN. . . . . . . . . . .      4.98%               4.99%(2)           4.81%     5.42%     3.75%      2.56%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . .     .77%                .88%(2)            .84%      .86%      .94%       .94%

   Ratio of net investment income

       to average net assets . . . . . . . .      4.88%               4.89%(2)           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 (000's Omitted) . $835,706            $903,313           $764,119  $654,581  $572,116   $616,072
- -----------------------------

(1) The Fund changed its fiscal year end from January 31 to November 30.
(2) Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS (CONTINUED)

  Contained  below is per share operating performance data for a share of Common
Stock  outstanding,  total  investment  return, ratios to average net assets and
other  supplemental  data  for  each period indicated. This information has been
derived from the Fund's financial statements.

                                                                                            Class B Shares
                                                                 _____________________________________________________________

                                                                Year Ended     Ten Months Ended

                                                               November 30,       November 30,        Year Ended January 31,
                                                                                                     ________________________

PER SHARE DATA:                                                    1998              1997(1)           1997           1996(2)
                                                              _____________    _________________       ______          ______

   Net asset value, beginning of period  . .                   $  1.00            $  1.00           $  1.00         $  1.00
                                                               _______            _______           _______         _______

   Investment Operations:

   Investment income--net  . . . . . . . . .                      .047               .039              .046            .043
                                                               _______            _______           _______         _______

   Distributions:

   Dividends from investment income--net . .                     (.047)             (.039)            (.046)          (.043)
                                                               _______            _______           _______         _______

   Net asset value, end of period  . . . . .                   $  1.00            $  1.00           $  1.00         $  1.00
                                                               =======            =======           =======         =======

TOTAL INVESTMENT RETURN. . . . . . . . . . .                      4.78%              4.83%(3)          4.65%           5.18%(3)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . .                    1.00%              1.00%(3)          1.00%           1.00%(3)

   Ratio of net investment income

       to average net assets . . . . . . . .                      4.66%              4.78%(3)          4.56%           5.00%(3)

   Decrease reflected in above expense ratios
       due to undertakings by the Manager  .                       .06%               .05%(3)           .07%            .07%(3)

   Net Assets, end of period (000's Omitted) . .            $2,427,332          $1,231,132         $369,205         $50,446
- -----------------------------

(1) The Fund changed its fiscal year end from January 31 to November 30.
(2) From March 31, 1995 (commencement of initial offering) to January 31, 1996.
(3) 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, 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.

  (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  $840  during  the  period  ended  November  30, 1998 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 are normally declared and
paid  annually,  but the Fund may make distributions on a more frequent basis to
comply with the distribution

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

requirements of the Internal Revenue Code of 1986, as amended (the "Code"). To
the  extent  that  net  realized  capital  gain  can  be  offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.

  (D)  FEDERAL INCOME TAXES: It is the policy of the Fund to continue to qualify
as  a  regulated  investment  company,  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  November 30, 1998, 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  November  30,  1998,  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 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 November 30,
1998, Class A shares were charged $1,724,844 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 November 30, 1998, Class B
shares were charged $3,564,210 pursuant to the Class B Distribution Plan.

GENERAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

(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  shareholder  accounts.  During  the  period ended November 30, 1998, Class A
shares were charged $240,310 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  had  undertaken from December 1, 1997 through November 30, 1998,
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  November  30,  1998,  $4,455,262 were charged
pursuant  to  the  Class  B  Shareholder  Services Plan, of which $1,046,213 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  November 30, 1998, the Fund was charged $263,144 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.


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
November  30,  1998,  and  the related statement of operations for the year then
ended,  and  the statement of changes in net assets 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  and  financial  highlights.  Our procedures included confirmation of
securities  owned  as  of November 30, 1998 by correspondence with the custodian
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 November 30, 1998 and the results of its
operations  for  the  year then ended, and the changes in its net assets and the
financial  highlights  for  each  of  the  indicated  years,  in conformity with
generally accepted accounting principles.

                                              [ERNST & YOUNG LLP SIGNATURE LOGO]






New York, New York
January 4, 1999


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                                   [reg.tm logo]

                                   (reg.tm)

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.

P.O. Box 9671

Providence, RI 02940











Printed in U.S.A.                                         196/696AR9811

General

Money Market

Fund, Inc.

Annual Report

November 30, 1998



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