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

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to  report the performance for General Government Securities
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 . . . . . . . . . .. . .       4.77%             4.88%

  Class B Shares . . . . . . . . . .. . .       4.57%             4.66%

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 GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    NOVEMBER 30, 1998

                                                                              Annualized
                                                                               Yield on
                                                                                Date of          Principal
U.S. Treasury Bills--2.1%                                                      Purchase           Amount          Value
                                                                               ________        ______________    ______________
<S>                                                                               <C>         <C>               <C>
___________________________________________________________________

  2/25/99

   (cost $24,733,639)  . . . . . . . . . . . . . . . . . . . . . . . . . .         4.51%       $   25,000,000   $    24,733,639

                                                                                                                 ==============

U.S. Government Agencies--92.4%

___________________________________________________________________

Federal Farm Credit Bank, Consolidated Systemwide Discount Notes:

   3/2/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.65%       $   50,000,000   $    49,981,451

   3/5/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.54            10,000,000         9,862,917

   5/3/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.96            23,860,000        23,919,827

   7/1/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.50            25,000,000        24,990,910

   11/8/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.81            20,000,000        19,127,900


Federal Farm Credit Bank, Consolidated Systemwide Floating Rate Notes:

   2/22/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.79(a)         50,000,000        49,994,472

   6/23/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.79(a)         50,000,000        49,983,627

   7/16/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.79(a)         25,000,000        24,990,671

   9/23/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.67(a)         25,000,000        25,000,000

   1/28/00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.82(a)         50,000,000        50,000,000

   2/9/00  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.80(a)         25,000,000        24,994,339

   3/17/00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.80(a)         50,000,000        49,987,861


Federal Home Loan Banks, Discount Notes:

   12/11/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.65            15,000,000        14,977,667

   1/29/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.42            15,618,000        15,486,436

   2/19/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.47            50,000,000        49,408,889

   3/23/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.57            25,000,000        24,994,093

   4/14/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.71            50,000,000        49,143,889

   6/11/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.63            25,000,000        24,989,611

   7/6/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.45            25,000,000        24,991,527

   7/9/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.48             9,650,000         9,342,165

   7/13/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.59            25,000,000        24,992,420


Federal Home Loan Mortgage Corporation, Discount Notes:

   2/16/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.74            50,000,000        49,500,568

   2/24/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.24            25,000,000        24,697,482


Federal National Mortgage Association, Discount Notes:

   3/1/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.30            20,000,000        19,741,500

   3/9/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.96            21,000,000        20,722,170

   5/10/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.91            25,000,000        24,470,000

   8/13/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.86            25,000,000        24,169,479

   8/20/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.45            17,000,000        16,360,356

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

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998

                                                                              Annualized
                                                                               Yield on
                                                                                Date of          Principal
U.S. Government Agencies (continued)                                           Purchase           Amount            Value
                                                                               ________        ______________    ______________

___________________________________________________________________

Federal National Mortgage Association, Floating Rate Notes

   4/15/99     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        4.78%(a)     $  100,000,000  $     99,978,326

   10/20/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.77(a)         25,000,000        25,000,000

   12/1/99     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         4.83(a)         50,000,000        50,000,000


Student Loan Marketing Association, Notes

   2/10/99     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.47            25,120,000        25,109,679

   6/2/99      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.55            50,000,000        49,998,042

   6/30/99     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         5.12            24,950,000        24,999,103

                                                                                                                 ______________


TOTAL U.S. GOVERNMENT AGENCIES (cost $1,095,907,377) . . . . . . . . . . .                                       $1,095,907,377
                                                                                                                 ==============

Repurchase Agreements--4.3%

___________________________________________________________________

Barclays De Zoette Wedd Securities, Inc.

  dated 11/30/98, due 12/1/98 in the amount of $4,575,565 (fully

  collateralized by $4,595,000 U.S. Treasury Notes 5.75% to

   6.375 %,  due 5/15/99 to 9/30/99, value $4,648,564) . . . . . . . . . .         4.45%      $     4,575,000    $    4,575,000


Goldman Sachs & Co.

  dated 11/30/98, due 12/1/98 in the amount of $7,001,011

  (fully collateralized by $6,945,000 U.S. Treasury Notes

   7.75%, due 11/30/99, value $7,149,009)  . . . . . . . . . . . . . . . .         5.20             7,000,000         7,000,000


SBC Warburg Dillon Read Inc.

  dated 11/30/98, due 12/1/98 in the amount of $40,005,889

  (fully collateralized by $41,718,000 U.S. Treasury Bills

   due 5/27/99, value $40,807,296) . . . . . . . . . . . . . . . . . . . .         5.30            40,000,000    $   40,000,000
                                                                                                                 ==============

TOTAL REPURCHASE AGREEMENTS (cost $51,575,000) . . . . . . . . . . . . . .                                       $   51,575,000
                                                                                                                 ==============

TOTAL INVESTMENTS (cost $1,172,216,016). . . . . . . . . . . . . .   98.8%                                       $1,172,216,016
                                                                  ========                                       ==============

CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . .      1.2%                                       $   13,646,575
                                                                  ========                                       ==============

NET ASSETS     . . . . . . . . . . . . . . . . . . . . . . . . . .  100.0%                                       $1,185,862,591
                                                                  ========                                       ==============



Notes to Statement of Investments:

___________________________________________________________________

(a) Variable interest rate--subject to periodic change.



                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>

GENERAL GOVERNMENT SECURITIES 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)  . . . . . . . . . . . . . . . .  $1,172,216,016       $1,172,216,016

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                            5,451,649

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                            9,092,423

                                 Prepaid expenses and other assets . . . . . . . . . . . .                               78,157
                                                                                                                _______________

                                                                                                                  1,186,838,245
                                                                                                                _______________


LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                              672,918

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                              125,205

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                              177,531

                                                                                                                _______________

                                                                                                                        975,654

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


NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       $1,185,862,591

                                                                                                                ===============



REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                       $1,186,029,702

                                 Accumulated net realized gain (loss) on investments . . .                             (167,111)

                                                                                                                _______________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       $1,185,862,591

                                                                                                                ===============



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

                                                                                                 Class A            Class B

                                                                                               _____________      _____________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $539,878,420       $645,984,171

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       540,012,775        646,016,929

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

                                                                                                      ======             ======

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>

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

STATEMENT OF OPERATIONS                          YEAR ENDED NOVEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                         <C>                   <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                                $56,682,802

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . .          $ 5,124,528

                                 Distribution fees--Note 2(b)  . . . . . . . . . .            2,049,811

                                 Shareholder servicing costs--Note 2(c)  . . . . .            1,652,767

                                 Registration fees . . . . . . . . . . . . . . . .              137,573

                                 Custodian fees  . . . . . . . . . . . . . . . . .               91,606

                                 Prospectus and shareholders' reports  . . . . . .               36,549

                                 Professional fees . . . . . . . . . . . . . . . .               34,700

                                 Director's fees and expenses--Note 2(d) . . . . .               33,273

                                 Miscellaneous . . . . . . . . . . . . . . . . . .                9,309

                                                                                            ___________

                                           Total Expenses  . . . . . . . . . . . .            9,170,116


                                 Less--reduction in shareholder servicing costs due to
                                    undertaking--Note 2(c) . . . . . . . . . . . .             (269,700)

                                                                                            ___________


                                           Net Expenses  . . . . . . . . . . . . .                                  8,900,416

                                                                                                                 ____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                 47,782,386

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . .                                        822

                                                                                                                 ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . .                                $47,783,208

                                                                                                                 ============


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>

GENERAL GOVERNMENT SECURITIES 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
                                                             ___________________   __________________      ________________
OPERATIONS:
<S>                                                             <C>                  <C>                   <C>
   Investment income--net  . . . . . . . . . . . . . . . . . .  $      47,782,386    $      31,426,952     $      27,816,414

   Net realized gain (loss) on investments . . . . . . . . . .                822              (86,200)              (67,319)
                                                                 ________________     ________________      ________________

          Net Increase (Decrease) in Net Assets Resulting
             from Operations . . . . . . . . . . . . . . . . .         47,783,208           31,340,752            27,749,095
                                                                 ________________     ________________      ________________
DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net:

       Class A Shares  . . . . . . . . . . . . . . . . . . . .        (25,243,444)         (20,661,515)          (24,381,410)

       Class B Shares  . . . . . . . . . . . . . . . . . . . .        (22,538,942)         (10,765,437)           (3,435,004)
                                                                 ________________     ________________      ________________

          Total Dividends  . . . . . . . . . . . . . . . . . .        (47,782,386)         (31,426,952)          (27,816,414)
                                                                 ________________     ________________      ________________

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

   Net proceeds from shares sold:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .      4,880,850,136        3,630,662,665         4,365,059,146

       Class B Shares  . . . . . . . . . . . . . . . . . . . .      1,928,335,745        1,175,920,736           318,478,705

   Dividends reinvested:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .         24,694,104           20,330,225            23,642,113

       Class B Shares  . . . . . . . . . . . . . . . . . . . .         21,778,602           10,538,441             3,417,531

   Cost of shares redeemed:
       Class A Shares  . . . . . . . . . . . . . . . . . . . .     (4,875,955,150)      (3,660,502,972)       (4,398,835,960)


       Class B Shares  . . . . . . . . . . . . . . . . . . . .     (1,668,976,351)        (911,764,032)         (231,770,578)
                                                                 ________________     ________________      ________________
          Increase (Decrease) in Net Assets from
             Capital Stock Transactions  . . . . . . . . . . .        310,727,086          265,185,063            79,990,957
                                                                 ________________     ________________      ________________

             Total Increase (Decrease) in Net Assets . . . . .        310,727,908          265,098,863            79,923,638

NET ASSETS:

   Beginning of Period . . . . . . . . . . . . . . . . . . . .        875,134,683          610,035,820           530,112,182
                                                                 ________________     ________________      ________________

   End of Period . . . . . . . . . . . . . . . . . . . . . . .    $ 1,185,862,591     $    875,134,683      $    610,035,820
                                                                 ================     ================      ================
- -------------------

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

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>

GENERAL GOVERNMENT SECURITIES 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  . . . . . . . . . . .          .048                .040           .047      .052      .038      .027
                                                       _______             _______        _______   _______   _______   _______

   Distributions:

   Dividends from investment income--net . . . .         (.048)              (.040)         (.047)    (.052)    (.038)    (.027)
                                                       _______             _______        _______   _______   _______   _______

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

TOTAL INVESTMENT RETURN. . . . . . . . . . . . .          4.88%               4.84%(2)       4.75%     5.35%     3.90%     2.69%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . .           .77%                .82%(2)        .82%      .84%      .83%      .81%

   Ratio of net investment income

       to average net assets . . . . . . . . . .          4.77%               4.78%(2)       4.65%     5.22%     3.82%     2.66%

   Net Assets, end of period (000's Omitted) . .      $539,878            $510,289       $519,861  $530,054  $513,345  $536,884
- -----------------------------

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

(2) Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL GOVERNMENT SECURITIES 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  . . . . . . . . .                         .046               .038             .045            .042
                                                                  _______            _______          _______         _______

   Distributions:

   Dividends from investment income--net . .                        (.046)             (.038)           (.045)          (.042)
                                                                  _______            _______          _______         _______

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


TOTAL INVESTMENT RETURN. . . . . . . . . . .                         4.66%              4.69%(3)         4.58%           5.04%(3)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . .                        .97%              1.00%(3)         1.00%           1.00%(3)

   Ratio of net investment income

       to average net assets . . . . . . . .                         4.55%              4.60%(3)         4.48%           5.01%(3)

   Decrease reflected in above expense ratios
       due to undertakings by the Manager  .                          .05%               .05%(3)          .08%            .10%(3)

   Net Assets, end of period (000's Omitted) . .                 $645,984           $364,845          $90,175             $58
- -----------------------------

(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 GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  General  Government  Securities  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 and the maintenance of liquidity.
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 16 billion shares of $.001 par value Common Stock. The
Fund  currently  offers  two  classes  of  shares:  Class  A  (15 billion shares
authorized)  and Class B (1 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  in securities 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  $32,626,  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 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.

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

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  (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 $172,000
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,  $19,000  of  the  carryover expires in fiscal 2003, $63,000 expires in
fiscal 2004 and $90,000 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
costs  of  preparing,  printing  and distributing prospectuses and statements of
additional  information and implementing and of operating the Plan. In addition,
Class  A shares reimburse (a) the Distributor for payments made for distributing
their  shares  and  servicing  shareholder  accounts  ("Servicing") and (b) the
Manager,  Dreyfus Service Corporation, a wholly-owned subsidiary of the Manager,
and  their  affiliates (collectively "Dreyfus") for payments made for Servicing,
at  an  aggregate  annual  rate  of  up  to .20 of 1% of the value of the Fund's
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 $1,058,316 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 Class B
shares  at  an  aggregate  annual  rate  of  up to .20 of 1% of the value of the
average  daily net assets of Class B. During the period ended November 30, 1998,
Class B shares were charged $991,495 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  the  Fund and
providing  reports  and  other  information.

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

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

and  services  related  to the maintenance of shareholder accounts. During the
period  ended November 30, 1998, Class A shares were charged $86,597 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 of the Fund, 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, Class B
shares  were  charged  $1,400,646  pursuant  to the Class B Shareholder Services
Plan, of which $269,700 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 $74,485, 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 GOVERNMENT SECURITIES MONEY MARKET FUND, INC.

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.

  We  have  audited  the  accompanying  statement  of  assets and liabilities of
General  Government  Securities 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, 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 Government Securities Money Market Fund, Inc., at November 30, 1998, and
the  results  of  its operations for the year then ended, 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 7, 1999


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

IMPORTANT TAX INFORMATION (UNAUDITED)

For State individual income tax purposes, the Fund hereby designates 54.75% of
the  ordinary  income  dividends  paid during its fiscal year ended November 30,
1998  as  attributable  to interest income from direct obligations of the United
States.  Such dividends are currently exempt from taxation for individual income
tax  purposes in most states, including New York, California and the District of
Columbia.


                                   [reg.tm logo]

                                   (reg.tm)

GENERAL GOVERNMENT SECURITIES

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.                                         975/698AR9811

General Government

Securities Money

Market Fund, Inc.

Annual Report

November 30, 1998





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