GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1998-02-04
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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.  Kindly take note that the fiscal year of
the Fund has been changed to conform with the reporting periods for other
money market funds in the General Family of Funds.  Accordingly, this annual
report covers the period from January 31, 1997, the date of the last annual
report, through the new fiscal year-end date, November 30, 1997.
    For that period of time, your Fund's performance is as shown in the
following chart:
<TABLE>                                                                                            ANNUALIZED
                                                                   ANNUALIZED YIELD             EFFECTIVE YIELD*
                                                                   ______________                _____________
<S>                                                                    <C>                           <C>
           Class A Shares.........................                      4.76%                        4.87%
           Class B Shares.........................                      4.60%                        4.70%
</TABLE>
The Economy
      Almost everything went right for the U.S. economy over the reporting
period. In its seventh year of expansion, the economy showed no sign of an
upsurge in inflation resulting from tightening labor markets. With the
unemployment rate at its lowest level in almost a decade, investors had been
concerned that wage gains might result in higher levels of inflation and
cause the Federal Reserve Board (the "Fed") to again raise interest rates.
Given the longevity of our economic recovery, the Fed's monetary policymakers
apparently were hoping that a cyclical easing in the economic growth rate
would help dampen any incipient inflationary pressure. Recent turmoil in the
financial markets of Asia and Latin America has raised prospects for a
slowdown in U.S. exports as those nations shore up their financial systems.
If this were to occur, the diminished demand for U.S. goods overseas could be
a drag on domestic economic growth. What is all but certain is that the Fed
is reluctant to further unsettle world financial markets by raising interest
rates over the near term.
    Indicators of future economic conditions showed high levels of consumer
optimism and pointed toward continued growth. Consumers' spirits have been
lifted by an unemployment rate at a quarter-century low (4.7% at the end of
the reporting period), and core inflation, which excludes food and energy
price changes, at the 2% level. The Conference Board, a business-sponsored
research group, recently reported that its Consumer Confidence Index hit a
new high for this economic expansion. Since consumers account for two thirds
of all economic activity, their confidence in the economy is an important
indicator of future conditions. Another important index of future economic
conditions, the Index of Leading Economic Indicators (also a Conference Board
index), implied continued growth. Government reports of personal income and
consumer spending showed healthy rates of increase as well.
    The production side of the economy continued its robust advance.
Industrial output rose consistently, and while the factory utilization rate
(a potential harbinger of production bottlenecks and price pressures) also
increased, there was little evidence of producer-generated inflation.
Additional good news regarding inflation came from the report that the
productivity of U.S. workers rose at its fastest pace in five years during
the third quarter of 1997. This increase in worker efficiency helped push down
 unit labor costs and eased concerns that labor costs, despite the tight
labor market, would lead to higher inflation.
    The interplay between worker productivity and worker wage increases does
much in determining the future course of inflation. We continue to monitor
that closely, along with developments in the international financial arena.
The recent international turbulence underscored the close economic
relationships that exist among all countries, particularly in this age of
multinational companies and pervasive global capitalism.
Money Market Overview
    During the past 12 months, money market rates have stayed within a
general trading range, fluctuating recently in response to pressure in the
overseas markets and a downturn in the U.S. stock market.  An inverse
relationship has emerged between money market instruments and equities.
The money market has provided an ideal liquidity haven for many investors.
    The last interest rate move by the Federal Reserve occurred in March
1997, when the Fed raised rates by a quarter point.  For a significant period
afterwards, the economy was moving at a moderate growth pace with subdued
inflation.  Later, concerns emerged regarding tight labor markets which
threatened to adversely affect the inflation outlook.  Recent evidence of
faster growth in several sectors of the economy drew a stronger case for
another Fed move.  If it were not for the recent difficulties occurring in
the overseas market and uncertainty over the effects on our economy, a policy
move would probably have been made. At its December meeting, the Fed voted to
keep the Fed Funds rate unchanged.
Portfolio Focus
    Against this backdrop, we have kept the average maturity of the portfolio
slightly longer than the industry average.  The intention has been to improve
yields without assuming undue market risks.  We believe that this strategy
has been beneficial to the Fund.  The currently volatile environment requires
flexibility on our part as managers.  Of course, we will make adjustments to
the portfolio strategy as required by the dynamics of the market.
                              Sincerely,

                            (Patricia A.Larkin SIGNATURE LOGO)
                              Patricia A. Larkin
                              Senior Portfolio Manager
December 18, 1997
New York, N.Y.
* Annualized 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, 1997
                                                                                  Annualized
                                                                                   Yield on
                                                                                     Date of       Principal
U.S. Treasury Bills-5.7%                                                            Purchase         Amount            Value
_______________________________________________________________________________    __________    _____________      ____________
<S>                                                                                    <C>          <C>              <C>

    1/22/98
    (cost $49,621,917).........................................                        5.29%     $  50,000,000      $  49,621,917
                                                                                                                    _____________
U.S. Government Agencies-78.0%
Federal Home Loan Banks, Discount Notes
    12/5/97....................................................                        5.49%     $   3,590,000      $   3,587,921
    1/13/98....................................................                        5.95         11,500,000         11,421,842
    3/27/98....................................................                        6.04         14,250,000         13,988,275
    6/8/98.....................................................                        5.60         17,338,000         16,848,288
    6/19/98....................................................                        5.62         10,440,000         10,127,380
    7/27/98....................................................                        5.62         25,000,000         24,109,153
Federal Home Loan Banks, Floating Rate Notes
    1/26/98....................................................                        5.74(a)       4,000,000          4,000,546
Federal Home Loan Banks, Notes
    1/21/98....................................................                        5.71          8,200,000          8,200,000
    1/22/98....................................................                        5.60         25,000,000         24,997,214
    3/17/98....................................................                        5.74         25,000,000         25,000,000
    9/24/98....................................................                        5.72         15,000,000         14,994,968
Federal Home Loan Mortgage Corp., Discount Notes
    1/2/98.....................................................                        5.58         17,900,000         17,813,682
Federal National Mortgage Association, Discount Notes
    12/4/97....................................................                        5.46         15,000,000         14,993,525
    12/15/97...................................................                        5.58         25,000,000         24,947,208
    4/6/98.....................................................                        5.52         25,000,000         24,530,125
    8/3/98.....................................................                        5.70         30,000,000         28,897,500
Federal National Mortgage Association, Floating Rate Notes
    1/21/98....................................................                        5.61(a)      10,000,000          9,999,279
    4/15/98....................................................                        5.63(a)     100,000,000         99,996,302
    9/15/98....................................................                        5.58(a)      75,000,000         74,953,658
    10/20/99...................................................                        5.52(a)      25,000,000         25,000,000
    12/1/99....................................................                        5.58(a)      50,000,000         50,000,000
Federal National Mortgage Association, Notes
    6/18/98....................................................                        5.67         50,000,000         50,013,503
    7/10/98....................................................                        5.70         10,000,000          9,965,469
    7/31/98....................................................                        5.61         25,000,000         24,991,712
Student Loan Marketing Association, Discount Notes
    6/30/98....................................................                        5.60         25,000,000         24,208,750
Student Loan Marketing Association, Notes
    5/15/98....................................................                        5.87         25,000,000        25,002,836
    12/4/98....................................................                        5.85         20,000,000        20,000,000
                                                                                                                   _____________
TOTAL U.S. GOVERNMENT AGENCIES (cost $682,589,136).............                                                    $ 682,589,136
                                                                                                                   =============
</TABLE>
<TABLE>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                   NOVEMBER 30, 1997
                                                                                  Annualized
                                                                                   Yield on
                                                                                    Date of        Principal
Repurchase Agreements-20.6%                                                        Purchase          Amount             Value
_______________________________________________________________________________   ___________    _____________     _____________
<S>                                                                                   <C>            <C>              <C>
Aubrey G.Lanston & Co. Inc.
    dated 11/28/97, due 12/1/97 in the amount of
    $69,032,488 (fully collateralized by
    $68,334,000 U.S. Treasury Notes 5.875%
    to 6.25% due from 4/30/98 to 6/30/98,
    value $69,917,310).........................................                        5.65%     $  69,000,000     $  69,000,000
Barclays De Zoette Wedd Securities, Inc.
    dated 11/28/97, due 12/1/97 in the amount of
    $34,016,008 (fully collateralized by
    $35,077,000 U.S. Treasury Bills due
    3/26/98, value $34,524,303)................................                        5.65         34,000,000        34,000,000
Bear, Stearns Cos. Inc.
    dated 11/28/97, due 12/1/97 in the amount of
    $5,002,383 (fully collateralized by
    $5,145,000 U.S. Treasury Bills due
    3/19/98, value $5,065,864).................................                        5.72          5,000,000         5,000,000
Morgan (J.P.) & Co.Inc.
    dated 11/28/97, due 12/1/97 in the amount of
    $34,016,093 (fully collateralized by
    $36,220,000 U.S. Treasury Bills due
    9/17/98, value $34,691,697)................................                        5.68         34,000,000        34,000,000
SBC Warburg Dillon Read Inc.
    dated 11/28/97, due 12/1/97 in the amount of
    $38,452,105 (fully collateralized by
    $39,456,000 U.S. Treasury Bills due
    from 1/2/98 to 5/28/98, value $39,220,136).................                        5.65         38,434,000        38,434,000
                                                                                                                   _____________
TOTAL REPURCHASE AGREEMENTS (cost $180,434,000)................                                                     $180,434,000
                                                                                                                   =============
TOTAL INVESTMENTS (cost $912,645,053)...............                    104.3%                                      $912,645,053
                                                                        ======                                     =============
LIABILITIES, LESS CASH AND RECEIVABLES..............                     (4.3%)                                     $(37,510,370)
                                                                        ======                                     =============
NET ASSETS..........................................                    100.0%                                      $875,134,683
                                                                        ======                                     =============
Notes to Statement of Investments:
_________________________________________________________________________________________________________________________________
    (a)  The interest rate, which will change periodically, is based on the
         bank's prime rate.
SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                         NOVEMBER 30, 1997
                                                                                                       Cost           Value
                                                                                                 _____________     _____________
<S>                                                                                               <C>                <C>
ASSETS:                Investments in securities-See Statement of Investments
                         (including Repurchase Agreements of
                         $180,434,000)-Note 1(b)...........................                      $ 912,645,053     $ 912,645,053
                       Cash................................................                                            1,978,843
                       Receivable for investment securities sold...........                                           25,000,000
                       Interest receivable.................................                                            6,120,304
                       Prepaid expenses and other assets...................                                              144,938
                                                                                                                   _____________
                                                                                                                     945,889,138
                                                                                                                   _____________
LIABILITIES:           Due to The Dreyfus Corporation and affiliates........                                             506,680
                       Due to Distributor...................................                                              20,511
                       Payable for investment securities purchased..........                                          70,000,000
                       Accrued expenses...........................                                                       227,264
                                                                                                                   _____________
                                                                                                                      70,754,455
                                                                                                                   _____________
NET ASSETS..................................................................                                        $875,134,683
                                                                                                                   =============
REPRESENTED BY:        Paid-in capital............................                                                  $875,302,616
                       Accumulated net realized gain (loss) on investments.....                                         (167,933)
                                                                                                                   _____________
NET ASSETS..................................................................                                        $875,134,683
                                                                                                                   =============
                                                          NET ASSET VALUE PER SHARE
                                                        _____________________________
                                                                                                    Class A           Class B
                                                                                                 _____________     _____________
Net Assets..................................................................                      $510,289,278      $364,845,405
Shares Outstanding..........................................................                       510,423,685       364,878,931

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
                                                                                             Ten Months End        Year Ended
                                                                                             November 30, 1997*  January 31, 1997
                                                                                             __________________  _______________
<S>                                                                                              <C>                <C>

INVESTMENT INCOME
INCOME                 Interest Income.........................                                  $37,306,665        $32,879,538
                                                                                                 ___________        ___________
EXPENSES:              Management fee-Note 2(a)................                                  $ 3,330,297        $ 3,002,777
                       Distribution fees-Note 2(b).............                                    1,332,119          1,201,111
                       Shareholder servicing costs-Note 2(c)...                                    1,000,318            543,687
                       Registration fees.......................                                      151,103            133,367
                       Custodian fees..........................                                      101,044            129,284
                       Professional fees.......................                                       48,870             44,394
                       Directors' fees and expenses-Note 2(d)..                                       26,924             36,549
                       Prospectus and shareholders' reports....                                        1,610             18,092
                       Miscellaneous...........................                                       ----               16,682
                                                                                                 ___________        ___________
                              Total Expenses                                                       5,992,285          5,125,943
                       Less-reduction in shareholder servicing costs due to
                           undertaking-Note 2(c)...............                                     (112,572)           (62,819)
                                                                                                 ___________        ___________
                              Net Expenses                                                         5,879,713          5,063,124
                                                                                                 ___________        ___________
INVESTMENT INCOME-NET................................................                             31,426,952         27,816,414
NET REALIZED GAIN (LOSS) ON INVESTMENTS-Note 1(b)....................                                (86,200)           (67,319)
                                                                                                 ___________        ___________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS.................                            $31,340,752        $27,749,095
                                                                                                 ===========        ===========
_______________________________
*    The Fund has 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.
STATEMENT OF CHANGES IN NET ASSETS
                                                                             Ten Months Ended    Year Ended         Year Ended
                                                                            November 30, 1997* January 31, 1997  January 31, 1996
                                                                          ___________________  ________________  _______________
<S>                                                                            <C>               <C>                <C>
OPERATIONS:
  Investment income-net...........................                            $  31,426,952      $  27,816,414     $  27,392,282
  Net realized gain (loss) on investments.........                                  (86,200)           (67,319)           (9,720)
                                                                              _____________      _____________     _____________
      Net Increase (Decrease) in Net Assets Resulting
        from Operations...........................                               31,340,752         27,749,095        27,382,562
                                                                              _____________      _____________     _____________
DIVIDENDS TO SHAREHOLDERS FROM:
  Investment income-net:
    Class A shares................................                              (20,661,515)       (24,381,410)      (27,390,125)
    Class B shares................................                              (10,765,437)        (3,435,004)           (2,157)
                                                                            _______________    _______________    _______________
      Total Dividends.............................                              (31,426,952)       (27,816,414)      (27,392,282)
                                                                            _______________    _______________    _______________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold:
    Class A shares................................                            3,630,662,665      4,365,059,146     4,619,394,913
    Class B shares................................                            1,175,920,736        318,478,705            97,286
  Dividends reinvested:
    Class A shares................................                               20,330,225         23,642,113        26,433,785
    Class B shares................................                               10,538,441          3,417,531             2,087
  Cost of shares redeemed:
    Class A shares................................                           (3,660,502,972)    (4,398,835,960)   (4,629,110,398)
    Class B shares................................                             (911,764,032)      (231,770,578)          (41,245)
                                                                            _______________    _______________    _______________
      Increase (Decrease) in Net Assets from
        Capital Stock Transactions................                              265,185,063         79,990,957        16,776,428
                                                                            _______________    _______________    _______________
            Total Increase (Decrease) in Net Assets                             265,098,863         79,923,638        16,766,708
NET ASSETS:
  Beginning of Period.............................                              610,035,820        530,112,182       513,345,474
                                                                            _______________    _______________   ________________
  End of Period...................................                          $   875,134,683    $   610,035,820   $   530,112,182
                                                                            ===============    ===============   ================
_______________________________
*The Fund has 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
                                                         _______________________________________________________________________
                                                          Ten Months Ended                Year Ended January 31,
                                                                                 ______________________________________________
PER SHARE DATA:                                          November 30, 1997(1)     1997      1996      1995      1994      1993
                                                         ___________________    _______   _______   _______   _______   _______
<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.................                             .040             .047      .052      .038      .027      .033
                                                               _______           _______   _______   _______   _______   ________
    Distributions:
    Dividends from investment income-net..                        (.040)           (.047)    (.052)    (.038)    (.027)    (.033)
                                                               _______           _______   _______   _______   _______   ________
    Net asset value, end of period........                     $  1.00           $  1.00   $  1.00   $  1.00   $  1.00   $  1.00
                                                               =======           =======   =======   =======   =======   ========
TOTAL INVESTMENT RETURN...................                        4.84%(2)          4.75%     5.35%     3.90%     2.69%     3.36%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets                        .82%(2)           .82%      .84%      .83%      .81%      .82%
    Ratio of net investment income
      to average net assets...............                        4.78%(2)          4.65%     5.22%     3.82%     2.66%     3.28%
    Net Assets, end of period (000's Omitted)                  $510,289          $519,861  $530,054  $513,345  $536,884  $725,419
_____________________________________
(1)    The Fund has changed its fiscal year end from January 31 to November 30.
(2)    Annualized.
SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
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
                                                                             ___________________________________________________
                                                                               Ten Months Ended            Year Ended January 31,
                                                                                                          ______________________
PER SHARE DATA:                                                               November 30, 1997(1)          1997       1996(2)
                                                                             ____________________         _______     _______
<S>                                                                                 <C>                    <C>         <C>
    Net asset value, beginning of period..................                          $  1.00               $  1.00     $  1.00
                                                                                    _______               _______     _______
    Investment Operations:
    Investment income-net.................................                              .038                  .045        .042
                                                                                    _______               _______     _______
    Distributions:
    Dividends from investment income-net..................                             (.038)                (.045)      (.042)
                                                                                    _______               _______     _______
    Net asset value, end of period........................                          $  1.00               $  1.00     $  1.00
                                                                                    =======               =======     =======
TOTAL INVESTMENT RETURN..................................                              4.69%(3)              4.58%       5.04%(3)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets..............                              1.00%(3)              1.00%       1.00%(3)
    Ratio of net investment income
      to average net assets..............................                              4.60%(3)              4.48%       5.01%(3)
    Decrease reflected in above expense ratios
      due to undertakings by the Manager.................                               .05%(3)               .08%        .10%(3)
    Net Assets, end of period (000's Omitted)............                           $ 364,845             $90,175      $58
__________________________________
(1)   The Fund has 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 ("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 ("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.
    The Fund has changed its fiscal year end from January 31 to November 30.
    (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.
    The Fund may enter into repurchase agreements with financial
institutions, deemed to be creditworthy by the Fund's Manager, subject to the
seller's agreement to repurchase and the Fund's agreement to resell such
securities at a mutually agreed upon price. Securities purchased subject to
repurchase agreements are deposited with the Fund's custodian and, pursuant
to the terms of the repurchase agreement, must have an aggregate market value
greater than or equal to the repurchase price plus accrued interest at all
times. If the value of the underlying securities falls below the value of the
repurchase price plus accrued interest, the Fund will require the seller to
deposit additional collateral by the next business day. If the request for
additional collateral is not met, or the seller defaults on its repurchase
obligation, the Fund maintains the right to sell the underlying securities at
market value and may claim any resulting loss against the seller.
    (c) Dividends to shareholders: It is the policy of the Fund to declare
dividends from investment income-net on each business day. Such dividends are
paid monthly. Dividends from net realized capital gain, if any, are normally
declared and paid annually, but the Fund may make distributions on a more
frequent basis to comply with the distribution requirements of the Internal
Revenue Code. To the extent that net realized capital gain can be offset by
capital loss carryovers, it is the policy of the Fund not to distribute such
gain.
    (d) Federal income taxes: It is the policy of the Fund to continue to
qualify as a regulated investment company, if such qualification is in the
best interests of its shareholders, by complying with the applicable
provisions of the Internal
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
Revenue Code, and to make distributions of taxable income sufficient to
relieve it from substantially all Federal income and excise taxes.
    The Fund has an unused capital loss carryover of approximately $83,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to January 31, 1997. The
carryover does not include net realized securities losses from November 1,
1996 through January 31, 1997 which are treated, for Federal income tax
purposes, as arising in fiscal 1998. If not applied, $20,000 of the carryover
expires in fiscal 2004 and $63,000 expires in fiscal 2005.
    At November 30, 1997, 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 periods ended January 31, 1997 and
November 30, 1997, 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, the Fund directly bears the
costs of preparing, printing and distributing prospectuses and statements of
additional information and implementing and of operating the Plan. In
addition, the Fund reimburses (a) the Distributor for payments made for
distributing Class A shares and servicing shareholder accounts ("Servicing")
and (b) the Manager, Dreyfus Service Corporation, a wholly-owned subsidiary
of the Manager, and their affiliates (collectively "Dreyfus") for payments
made for Servicing, at an aggregate annual rate of up to .20 of 1% of the
value of the 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 periods ended January 31, 1997 and
November 30, 1997, the Fund was charged $1,047,607 and $867,630,
respectively, 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, the Fund
directly bears the costs of preparing, printing and distributing prospectuses
and statements of additional information and of implementing and operating
the Class B Distribution Plan. In addition, the Fund reimburses the
Distributor for payments made to third parties for distributing Class B
shares at an aggregate annual rate of up to .20 of 1% of the value of the
average daily net assets of Class B. During the periods ended January 31,
1997 and November 30, 1997, the Fund was charged $153,504 and $464,489,
respectively, pursuant to the Class B Distribution Plan.
    (c) Under the Fund's Shareholder Services Plan with respect to Class A
("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus Service
Corporation an amount not to exceed an annual rate of .25 of 1% of the value
of the Fund's average daily net assets of Class A for certain allocated
expenses of providing personal services and/or maintaining shareholder
accounts. The services provided may include personal services relating to
shareholder accounts, such as
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
answering shareholder inquiries regarding the Fund and providing reports and
other information, and services related to the maintenance of shareholder
accounts. During the periods ended January 31, 1997 and November 30, 1997,
the Fund was charged $215,006 and $228,811, respectively, 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"), the Fund pays the Distributor for the
provision of certain services to the holders of Class B shares a fee at an
annual rate of .25 of 1% of the value of the average daily net assets of
Class B. The services provided may include personal services relating to
shareholder accounts, such as answering shareholder inquiries regarding the
Fund and providing reports and other information, and services related to the
maintenance of shareholder accounts. The Distributor may make payments to
Service Agents in respect of these services. The Distributor determines the
amounts to be paid to Service Agents.
    The Manager has undertaken, through January 31, 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 periods ended January 31, 1997 and
November 30, 1997, the Fund was charged $191,880 and $580,611, respectively,
pursuant to the Class B Shareholder Services Plan, of which $62,819 and
$112,572, respectively, 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
periods ended January 31, 1997 and November 30, 1997, the Fund was charged
$58,897 and $50,005, respectively, 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, 1997, and the related statements
of operations for each of the two years in the period then ended, the
statement of changes in net assets for each of the three years in the period
then ended and financial highlights for each of the years indicated therein.
These financial statements and financial highlights are the responsibility of
the Fund's management. Our responsibility is to express an opinion on these
financial statements and financial highlights based on our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements and financial highlights. Our procedures included
confirmation of securities owned as of November 30, 1997 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, 1997, and the results of its operations for each of the two
years in the period then ended, the changes in its net assets for each of the
three years in the period then ended and the financial highlights for each of
the indicated years, in conformity with generally accepted accounting
principles.

                          [ERNST & YOUNG LLP signature logo]

New York, New York
January 8, 1998



Registration Mark
[Dreyfus lion "d" logo]
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.                       975/698AR9711
General
Government
Securities Money
Market Fund, Inc.
Annual Report
November 30, 1997
Registration Mark
[Dreyfus logo]



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