GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1998-08-07
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                                   (reg.tm)

                                   (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.                                          975/698SA985

General Government

Securities Money

Market Fund, Inc.

Semi-Annual Report

May 31, 1998




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 for the six-month period ended May 31, 1998, as shown in the
following table:

                                                                 ANNUALIZED
                                            ANNUALIZED YIELD   EFFECTIVE YIELD*
                                            ________________   ________________

        Class A Shares                         4.84%                4.95%

        Class B Shares                         4.64%                4.74%

The Economy

  Although   real   Gross  Domestic  Product  (GDP)  sustained  a  growth  trend
approaching  4%  into  the  first  quarter,  recent evidence suggests a shift to
somewhat  slower  economic  growth  in  coming  months. Aggregate profit margins
already  have  begun  to  narrow in some sectors. The conflicting pressures of a
softening  economy dampened by the Asian financial crisis and a tightening labor
market  have  kept  the Federal Reserve Board (the "Fed") in neutral, although a
bias  towards  higher  rates  was  reinstated  at  the March 1998 meeting of the
Federal  Open  Market  Committee  (the  policy-making  arm  of  the Fed). Market
interest rates have likewise stayed within a narrow range in recent months.

  While  manufacturing  has turned appreciably sluggish since year end, this was
overshadowed  in  the  first quarter by a strong rebound in domestic demand. The
industrial  sector  has  been  slowed  by the strong dollar and by weak exports.
However,  with  Asian  economies  still  in turmoil, competition from Asian-made
imports  has  emerged  slowly.  The first quarter rebound in domestic demand was
fueled  primarily  by strong housing market conditions and rising real household
incomes.

  Rising real wages that have been such a boon to consumers in recent months may
take  a  toll on corporate profit margins. The first sign of profit pressure was
seen last year as the dollar strengthened. This year, profit margins have eroded
further  due  to  weak  exports and falling prices in some sectors. Accelerating
wage growth alongside limited pricing power may also prove a harbinger of profit
margin  erosion.  Hence,  a  shift  to slower economic growth that coexists with
rising  wage  pressures  creates  a  further  risk  to  overall  profit  growth.

  The  above  pressures  have  kept  Fed policy unchanged until now. However, it
appears  that  policymakers  are  more  concerned  about  wage growth than about
economic  strains,  as  evidenced  by  a recent shift towards a tightening bias.
Although  long-term  bond  yields  were below year-ago levels at the end of May,
substantially  lower  yields  have  proven difficult to attain in the absence of
lower short-term rates. This too could restrain the economic growth rate.

The Market Environment

  For  the  past  six  months,  expectations  for short-term interest rates have
fluctuated  between  the need for an increase in the Federal Funds rate in order
to  cool  off  an  overheating  economy,  and for an ease in order to offset the
Asian-crisis-triggered slowdown. Government securities are currently in a narrow
band and likely to remain there until a clear trend develops.

  As  the  economy  continues into its seventh year of expansion, the short-term
money  markets  are  also  on  the  lookout for signs that the economic cycle is
coming to an end. With unemployment at historic lows, the market is on alert for
a  labor  shortage-inspired  pickup  in  inflation.   To date, there has been no
evidence of such an occurrence.

  Another  development  that  gives  many  market  participants  concern  is the
increasing talk of an "asset bubble." The short-term market is apprehensive that
Federal  Reserve  chairman  Alan  Greenspan,  concerned  over the effects of the
dramatic rise in stock prices, will raise short-term rates in an attempt to head
off the speculative excesses that might derail the economy.

  With  economic  releases  providing  an  often  contradictory  picture  of the
economy, the financial markets are especially sensitive to comments from Federal
Reserve  members.  Recent  speeches  suggest that the Fed is concerned about the
possibility of re-emerging inflationary pressures, yet is prepared to wait until
a more definitive picture develops before altering monetary policy.

Portfolio Focus

  In  this  market  environment, we continue to maintain an average maturity for
the  Fund  which is somewhat longer than the industry average. We feel that this
strategy  has  been  beneficial to the Fund, and we currently intend to maintain
that  posture  as  long  as we believe it corresponds with market conditions. Of
course,  we  will  look  to  adapt our approach should new factors in the market
cause us to believe that such action is desirable.

               Sincerely,





               Patricia A. Larkin

               Senior Portfolio Manager

June 18, 1998

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>
<CAPTION>

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

STATEMENT OF INVESTMENTS                             MAY 31, 1998 (UNAUDITED)

                                                                              Annualized
                                                                               Yield on
                                                                                Date of        Principal
U.S. Treasury Notes--1.6%                                                       Purchase         Amount             Value
- ---------------------------------------------------------------------------   ____________    _____________     _____________
   <S>                                                                          <C>             <C>               <C>
   5.875% 10/31/98
       (cost $15,017,593)..................................................     5.37%           $  15,000,000     $  15,017,593
                                                                                                                _____________
                                                                                                                _____________
U.S. Government Agencies--97.2%
- ----------------------------------------------

Federal Farm Credit Bank, Consolidated Systemwide Discount Notes
   11/24/98................................................................     5.69%             $24,000,000       $23,365,227
   3/2/99..................................................................      5.56              50,000,000        49,944,149
   3/5/99..................................................................      5.54              10,000,000         9,596,042
Federal Farm Credit Bank, Consolidated Systemwide Floating Rate Notes
   2/22/99.................................................................      5.54 (a)          50,000,000        49,982,282
   1/28/00.................................................................      5.57 (a)          50,000,000        50,000,000
   2/9/00..................................................................      5.55 (a)          25,000,000        24,991,958
   3/17/00.................................................................      5.55 (a)          50,000,000        49,983,155
Federal Home Loan Banks, Discount Notes
   6/1/98..................................................................      5.45               9,726,000         9,726,000
   6/5/98..................................................................      5.72              50,000,000        49,969,083
   6/8/98..................................................................      5.60              17,338,000        17,319,863
   6/19/98.................................................................      5.62              10,440,000        10,411,864
   7/9/98..................................................................      5.36               8,500,000         8,453,165
   7/27/98.................................................................      5.62              25,000,000        24,790,389
   9/24/98.................................................................      5.72              15,000,000        14,998,052
   12/11/98................................................................      5.65              15,000,000        14,568,967
   1/29/99.................................................................      5.42              15,618,000        15,078,363
   3/23/99.................................................................      5.58              25,000,000        24,984,442
Federal Home Loan Banks, Notes
   4/23/99.................................................................      5.61              25,000,000        25,003,489
Federal National Mortgage Association, Discount Notes
   6/18/98.................................................................      5.67              50,000,000        50,001,154
   7/10/98.................................................................      5.70              10,000,000         9,993,905
   7/31/98.................................................................      5.61              25,000,000        24,997,944
   8/3/98..................................................................      5.70              30,000,000        29,716,500
Federal National Mortgage Association, Floating Rate Notes
   9/15/98.................................................................      5.58 (a)          75,000,000        74,982,943
   4/15/99.................................................................      5.53 (a)         100,000,000        99,948,946
   10/20/99................................................................      5.52 (a)          25,000,000        25,000,000
   12/1/99.................................................................      5.58 (a)          50,000,000        50,000,000

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

STATEMENT OF INVESTMENTS (continued)                MAY 31, 1998 (UNAUDITED)

                                                                              Annualized
                                                                               Yield on
                                                                                Date of        Principal
U.S Government Agencies (continued)                                             Purchase         Amount             Value
- ---------------------------------------------------------------------------   ____________    _____________       _____________

Student Loan Marketing Association, Discount Notes
   6/30/98.................................................................     5.60%           $  25,000,000     $  24,891,250
Student Loan Marketing Association, Notes
   2/10/99.................................................................      5.47              25,120,000        25,083,076
                                                                                                                  _____________

TOTAL U.S. GOVERNMENT AGENCIES (cost $887,782,208).........................                                        $887,782,208
                                                                                                                  _____________
                                                                                                                  _____________

TOTAL INVESTMENTS (cost $902,799,801)............................      98.8%                                       $902,799,801
                                                                      ======                                      =============

CASH AND RECEIVABLES (NET).......................................       1.2%                                      $  10,369,036
                                                                      ======                                      =============
NET ASSETS.......................................................     100.0%                                       $913,168,837
                                                                      ======                                      =============
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>
<CAPTION>


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

STATEMENT OF ASSETS AND LIABILITIES                  MAY 31, 1998 (UNAUDITED)

                                                                                                   Cost              Value

                                                                                              ________________   _____________
<S>                                                                                              <C>               <C>

ASSETS:                          Investments in securities--See Statement of Investments.......  $902,799,801      $902,799,801
                                 Cash..........................................................                       3,870,149
                                 Interest receivable...........................................                       7,236,311
                                 Prepaid expenses and other assets.............................                          66,051
                                                                                                                  _____________
                                                                                                                    913,972,312
                                                                                                                  _____________
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates.................                         541,300
                                 Due to Distributor............................................                         115,302
                                 Accrued expenses..............................................                         146,873
                                                                                                                  _____________
                                                                                                                        803,475
                                                                                                                  _____________
NET ASSETS.....................................................................................                    $913,168,837
                                                                                                                  _____________
                                                                                                                  _____________
REPRESENTED BY:                  Paid-in capital...............................................                    $913,340,411
                                 Accumulated net realized gain (loss) on investments...........                       (171,574)
                                                                                                                  _____________
NET ASSETS.....................................................................................                    $913,168,837
                                                                                                                  =============
</TABLE>
<TABLE>
<CAPTION>


                           NET ASSET VALUE PER SHARE
                            _____________________________

                                                                                                 Class A           Class B

                                                                                               ______________     _____________
<S>                                                                                              <C>               <C>
Net Assets.....................................................................................  $519,098,447      $394,070,390
Shares Outstanding.............................................................................   519,234,918       394,105,494
NET ASSET VALUE PER SHARE......................................................................         $1.00             $1.00
                                                                                                        =====             =====

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


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

STATEMENT OF OPERATIONS             SIX MONTHS ENDED MAY 31, 1998 (UNAUDITED)

INVESTMENT INCOME
<S>                         <C>                                                                  <C>                <C>

INCOME                      Interest Income....................................................                     $25,665,191
EXPENSES:                   Management fee--Note 2(a)..........................................  $  2,279,768
                            Distribution fees (Class B)--Note 2(b).............................       911,907
                            Shareholder servicing costs--Note 2(c).............................       694,862
                            Registration fees..................................................        77,625
                            Custodian fees.....................................................        46,992
                            Directors' fees and expenses--Note 2(d)............................        17,885
                            Professional fees..................................................        14,456
                            Prospectus and shareholders' reports...............................        12,357
                                                                                                  ____________
                                   Total Expenses..............................................     4,055,852
                            Less--reduction in shareholder servicing costs due to
                                undertaking--Note 2(c).........................................      (90,131)
                                                                                                  ____________
                                   Net Expenses................................................                       3,965,721
                                                                                                                    ____________
INVESTMENT INCOME--NET.........................................................................                      21,699,470
NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b)..............................                         (3,641)
                                                                                                                    ____________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS...........................................                     $21,695,829
                                                                                                                    ============


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


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

STATEMENT OF CHANGES IN NET ASSETS

                                                                 Six Months Ended

                                                                    May 31,1998        Ten Months Ended        Year Ended
                                                                    (Unaudited)       November 30, 1997*    January 31, 1997
                                                                 __________________   __________________    __________________
<S>                                                               <C>                  <C>                   <C>
OPERATIONS:
  Investment income--net....................................      $     21,699,470     $     31,426,952      $     27,816,414
  Net realized gain (loss) on investments...................                (3,641)             (86,200)              (67,319)
                                                                   _______________       _______________      _______________
       Net Increase (Decrease) in Net Assets Resulting
         from Operations....................................            21,695,829           31,340,752            27,749,095
                                                                   _______________       _______________      _______________
DIVIDENDS TO SHAREHOLDERS FROM:
 Investment income--net:
    Class A shares..........................................          (12,681,580)         (20,661,515)          (24,381,410)
    Class B shares..........................................           (9,017,890)         (10,765,437)           (3,435,004)
                                                                   _______________       _______________      _______________
       Total Dividends......................................          (21,699,470)         (31,426,952)          (27,816,414)
                                                                   _______________       _______________      _______________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
 Net proceeds from shares sold:
    Class A shares..........................................         2,353,493,947        3,630,662,665         4,365,059,146
    Class B shares..........................................           822,248,569        1,175,920,736           318,478,705
  Dividends reinvested:
    Class A shares..........................................            12,386,548           20,330,225            23,642,113
    Class B shares..........................................             8,653,687           10,538,441             3,417,531
  Cost of shares redeemed:
    Class A shares..........................................        (2,357,069,262)      (3,660,502,972)       (4,398,835,960)
    Class B shares..........................................          (801,675,694)        (911,764,032)         (231,770,578)
                                                                   _______________       _______________      _______________
       Increase (Decrease) in Net Assets from...............            38,037,795          265,185,063            79,990,957
                                                                   _______________       _______________      _______________
         Capital Stock Transactions
            Total Increase (Decrease) in Net Assets.........            38,034,154          265,098,863            79,923,638
NET ASSETS:
  Beginning of Period.......................................           875,134,683          610,035,820           530,112,182
                                                                   _______________       _______________      _______________
  End of Period.............................................       $   913,168,837      $   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>
<PAGE>
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.
<TABLE>
<CAPTION>



                                                                              Class A Shares

                                           _____________________________________________________________________________________
_____________________

                                           Six Months Ended   Ten Months Ended
                                             May 31, 1998       November 30,                 Year Ended January 31,
                                                                               _____________________________________________
PER SHARE DATA:                              (Unaudited)          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....................    .024            .040               .047        .052        .038         .027
                                               _________       __________         _________    _________  __________   __________
   Distributions:
   Dividends from investment income--net.....   (.024)          (.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......................   4.89%(2)        4.84%(2)           4.75%       5.35%       3.90%        2.69%
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets...    .77%(2)         .82%(2)            .82%        .84%        .83%         .81%
   Ratio of net investment income
       to average net assets.................   4.85%(2)        4.78%(2)           4.65%       5.22%       3.82%        2.66%
   Net Assets, end of period (000's Omitted). $519,098        $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.
<PAGE>
</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.
<TABLE>
<CAPTION>



                                                                                        Class B Shares

                                                       _________________________________________________________________________

                                                       Six Months Ended
                                                         May 31, 1998            Ten Months Ended      Year Ended January 31,
                                                                                                       _______________________

PER SHARE DATA:                                           (Unaudited)          November 30, 1997(1)     1997           1996(2)
                                                       ________________        ___________________     _______         _______
   <S>                                                       <C>                       <C>             <C>             <C>
   Net asset value, beginning of period................      $  1.00                   $  1.00         $ 1.00          $ 1.00
   Investment Operations:
   Investment income--net..............................          .023                      .038           .045            .042
                                                            _________                  ________        _______         _______
   Distributions:
   Dividends from investment income--net...............       (.023)                    (.038)          (.045)           (.042)
                                                            _________                  ________        _______         _______

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

TOTAL INVESTMENT RETURN................................         4.69%(3)                  4.69%(3)        4.58%            5.04%(3)
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets.............         1.00%(3)                  1.00%(3)        1.00%            1.00%(3)
   Ratio of net investment income
       to average net assets...........................         4.64%(3)                  4.60%(3)        4.48%            5.01%(3)
   Decrease reflected in above expense ratios
       due to undertakings by the Manager..............          .05%(3)                   .05%(3)         .08%             .10%(3)
   Net Assets, end of period (000's Omitted)...........     $394,070                  $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.
</TABLE>

                      SEE NOTES TO FINANCIAL STATEMENTS.

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

NOTES TO FINANCIAL STATEMENTS (UNAUDITED)

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.

  (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  custodian  agreement, the Fund received net earnings
credits  of $19,981 during the period ended May 31, 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
<PAGE>

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

NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

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  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  May  31, 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  May  31,  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 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
<PAGE>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

with whom the Service Agent has a Servicing relationship or for whom the Service
Agent is the dealer or holder of record. The schedule of such fees and the basis
upon  which  such fees will be paid shall be determined from time to time by the
Fund' s  Board of Directors. If a holder of Class A shares ceases to be a client
of  a  Service  Agent,  but  continues  to  hold Class A shares, Dreyfus will be
permitted  to  act  as  a Service Agent in respect of such Fund shareholders and
receive  payments  under  the  Service  Plan for Servicing. The fees payable for
Servicing  are  payable  without  regard to actual expenses incurred. During the
period ended May 31, 1998, Class A shares were charged $523,393, 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 May 31, 1998, Class
B shares were charged $388,514 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  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, and services related to the maintenance
of  shareholder  accounts.  During the period ended May 31, 1998, Class A shares
were charged $29,181, pursuant to the Class A Shareholder Services Plan.

  Under  the  Fund's Shareholder Services Plan with respect to Class B ("Class B
Shareholder  Services  Plan" ), Class  B  shares  pay  the  Distributor  for the
provision  of  certain  services  to  the  holders of Class B shares a fee at an
annual  rate  of .25 of 1% of the value of the average daily net assets of Class
B.  The  services provided may include personal services relating to shareholder
accounts,  such  as answering shareholder inquiries regarding Class B shares and
providing reports and other information, and services related to the maintenance
of  shareholder accounts. The Distributor may make payments to Service Agents in
respect  of these services. The Distributor determines the amounts to be paid to
Service Agents.

The Manager has undertaken from December 1, 1997 through May 31, 1998, that if
the  aggregate  expenses  of  Class  B  shares,  exclusive  of taxes, brokerage,
interest on borrowings and extraordinary expenses, exceed 1% of the value of the
average  daily net assets of Class B, the Manager will reimburse the expenses of
the Fund under the Class B Shareholder Services Plan to the extent of any excess
expense  and  up  to the full fee payable under the Class B Shareholder Services
Plan.  During  the  period  ended  May  31,  1998,  Class  B shares were charged
$582,771,  pursuant  to  the Class B Shareholder Services Plan, of which $90,131
was reimbursed by the Manager.
<PAGE>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

  The  Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,  under  a  transfer  agency  agreement,  for  providing  personnel  and
facilities  to  perform transfer agency services for the Fund. During the period
ended  May  31, 1998, the Fund was charged $000, 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.



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