GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1996-09-26
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GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on General Government
Securities Money Market Fund, Inc. For its semi-annual reporting period ended
July 31, 1996, your Fund produced annualized yields of 4.68% for Class A
shares and 4.49% for Class B shares. Reinvesting dividends and calculating
the effect of compounding resulted in annualized effective yields of 4.78%
and 4.58% for Class A shares and Class B shares, respectively.*
ECONOMIC REVIEW
    U.S. economic growth accelerated in the first half of 1996 after 1995's
slowdown. However, this year's faster economy is accompanied by reports of
slowing corporate profit growth. Faster growth fostered fears of higher
future inflation, even while reported inflation remained tame. The fear of
inflation, as distinguished from the reality, pushed bond yields higher and
raised expectations of a Federal Reserve Board ("Fed") tightening. Some of
these fears have receded recently on evidence indicating a softer economy in
the summer months.
    This year's reacceleration in the economy was due to a sharp rebound in
domestic demand that left inventories lean. Real Gross Domestic Product grew
2.0% and 4.2% in the first and second quarters, respectively, driven largely
by consumer spending and housing investment. Industrial output growth
likewise strengthened as producers tried to replenish inventory. The faster
economy has fueled steady job creation that sustains support for consumers'
incomes and spending power. However, economic strength has not been
broadbased: exports are slow and some previously strong capital goods sectors
have weakened. Moreover, early evidence on the third quarter indicates a
slower profile for spending and production this summer. Despite faster
overall economic growth this year, the peak in profit growth for this cycle
may already have occurred last year.
    Wage increases accelerated in this year's tight labor market, which added
to the case for renewed inflation. Thus, bond yields rose substantially.
Short-term market rates also surged on expectation of a Fed tightening, but
have since retreated. So far, long-term rates have risen much more than
short-term rates, forcing the yield curve to steepen. A steep yield curve is
usually supportive of sustained growth in the real economy.
    The debate over whether the economy might slow down in the near term
without a Fed tightening appears to be resolved by incoming evidence of a
sluggish summer economy. Nevertheless, fundamentals remain supportive of
sustained growth. Household income growth is robust and supportive of
sustained demand growth. And inventories are lean, which can lead to
sustained production growth. Summer sluggishness, however, would keep
inflation fears at bay, deferring expectations for a Fed tightening out into
the future.
THE MONEY MARKET AND THE PORTFOLIO
    A year ago, the main concern of monetary policy makers was whether the
U.S. economy would head into a recession. Unemployment figures were
stubbornly high, profits were slack, and the economic growth rate slowed
noticeably. The Fed addressed these problems with a succession of steps to
reduce short-term interest rates, the last such step being taken at the end
of January, 1996.

    Since then, the central bank authorities appear to have stepped away from
such an active management role. The economy has strengthened on its own, with
the marketplace exerting more force than Government actions.
    As explained in the previous section of this report, the strength shown
by the economy has brought policy expectations full circle. The market now is
apprehensive about a tightening in interest rates by the Fed and certainly
does not expect the Fed to loosen the credit reins.
    As spring gave way to summer, there were a succession of economic
indicators showing a stronger tone in the economy, yet without imminent
danger of runaway price or wage inflation. Early in the spring and summer,
the money market was jolted by early signs of economic revival such as strong
employment numbers. By July, however, the market appeared to take such
indications more in stride, especially now that the latest figures point to a
more subdued rate of growth.
    As the latest semi-annual period ended, the money market appeared
prepared for possible tightening moves by the Fed, but not necessarily any
imminent action. If the present course of slower growth continues, it might
not be necessary for the Fed to flex its muscles until after the November
elections.
    We have been vigilant in keeping an eye on the changing tone of the
market.
    Bearing all this in mind, we intend to maintain our policy of somewhat
longer portfolio maturities until we see clearer signs that a more defensive
policy should be instituted.
    We appreciate the opportunity to manage money on your behalf and will
continue our best efforts to bring you rewarding returns.
                              Sincerely,
                          [Patricia A. Larkin signature logo]
                              Patricia A. Larkin
                              Senior Portfolio Manager
August 13, 1996
New York, N.Y.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
<TABLE>
<CAPTION>


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                        JULY 31, 1996 (UNAUDITED)
                                                                         ANNUALIZED
                                                                          YIELD ON
                                                                           DATE OF         PRINCIPAL
U.S. TREASURY BILLS-10.6%                                                  PURCHASE          AMOUNT                 VALUE
                                                                           ______          _____________       ________________
    <S>                                                                      <C>           <C>                 <C>
    8/22/96....................................................              5.80%         $35,000,000         $  34,888,117
    3/6/97.....................................................              5.40           10,000,000             9,690,775
    5/1/97.....................................................              5.58           20,000,000            19,199,200
                                                                                                                 ____________
TOTAL U.S. TREASURY BILLS (cost $63,778,092)...................                                                $  63,778,092
                                                                                                             ================
U.S. GOVERNMENT AGENCIES-81.7%
Federal Farm Credit Bank, Floating Rate Notes
    9/3/96.....................................................              5.63%(a)      $50,000,000          $  50,000,000
    9/16/96....................................................              5.43(a)        25,000,000            24,999,652
    11/7/96....................................................              5.33(a)        15,000,000            14,996,126
    7/25/97....................................................              5.33(a)        15,000,000            14,994,377
    9/15/97....................................................              5.38(a)        15,000,000            14,992,117
Federal Home Loan Banks, Discount Notes
    2/19/97....................................................              5.67           25,000,000            24,229,875
    4/2/97.....................................................              5.52           10,000,000             9,997,392
    4/25/97....................................................              5.70           25,000,000            24,997,256
Federal Home Loan Banks, Floating Rate Notes
    1/26/98....................................................              5.49(a)         4,000,000             4,005,298
Federal Home Loan Banks, Notes
    11/7/96....................................................              5.46           15,000,000            14,999,213
    11/20/96...................................................              5.40           10,000,000             9,996,395
    3/5/97.....................................................              5.23           15,000,000            15,000,000
    3/6/97.....................................................              5.22           25,000,000            24,996,477
    6/27/97....................................................              5.90            7,680,000             7,671,876
Federal National Mortgage Association, Discount Notes
    9/18/96....................................................              5.31           20,000,000            19,863,733
    1/21/97....................................................              5.59           43,000,000            41,877,951
Federal National Mortgage Association, Floating Rate Notes
    10/4/96....................................................              5.70(a)        25,000,000            25,000,000
    12/16/96...................................................              5.40(b)        10,000,000             9,996,364
    1/13/97....................................................              5.43(a)        15,000,000            15,000,000
    3/14/97....................................................              5.30(a)        25,000,000            25,000,000
    6/20/97....................................................              5.46(a)        20,000,000            19,998,350
    7/25/97....................................................              5.37(a)        20,000,000            20,000,000
    8/18/97....................................................              5.38(a)        30,000,000            29,995,297
    1/21/98....................................................              5.36(a)        10,000,000             9,992,397
Student Loan Marketing Association, Floating Rate Notes
    12/20/96...................................................              5.46(b)        18,000,000            18,000,000
                                                                                                                 ___________
TOTAL U.S. GOVERNMENT AGENCIES (cost $490,600,146).............                                                 $490,600,146
                                                                                                               ==============

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                            JULY 31, 1996 (UNAUDITED)
                                                                           ANNUALIZED
                                                                            YIELD ON
                                                                             DATE OF        PRINCIPAL
REPURCHASE AGREEMENTS-6.7%                                                   PURCHASE         AMOUNT             VALUE
                                                                           ______           ___________        ____________
Barclays De Zoette Wedd Securities,Inc.
    dated 7/31/96, due 8/1/96 in the amount of
    $11,522,920 (fully collateralized by
    $11,720,000 U.S. Treasury Bills due 8/15/96,
    value $11,696,511).........................................              6.00%         $11,521,000         $  11,521,000
Morgan Stanley & Company, Inc.
    dated 7/31/96, due 8/1/96 in the amount of
    $10,001,556 (fully collateralized by
    $9,810,000 U.S. Treasury Notes 6.88%, due 2/28/97,
    value $10,156,616).........................................              5.60           10,000,000            10,000,000
SBC Capital Markets, Inc.
    dated 7/31/96, due 8/1/96 in the amount of
    $19,003,000 (fully collateralized by
    $19,606,000 U.S. Treasury Bills due 10/17/96,
    value $19,387,230).........................................              5.68           19,000,000            19,000,000
                                                                                                              ______________
TOTAL REPURCHASE AGREEMENTS (cost $40,521,000).................                                                $  40,521,000
                                                                                                              ===============
TOTAL INVESTMENTS (cost $594,899,238).................                      99.0%                               $594,899,238
                                                                           ======                            ===============
CASH AND RECEIVABLES (NET)............................                        1.0%                            $    5,763,582
                                                                           ======                            ===============
NET ASSETS............................................                    100.0%                                $600,662,820
                                                                           ======                            ===============

NOTES TO STATEMENT OF INVESTMENTS:
    (a)  The interest rate, which will change periodically, is based on the
    bank's prime rate.
    (b)  Variable interest rates-subject to change approximately every 7 to
    30 days.

</TABLE>





See independent accountants' review report and notes to financial statements.
<TABLE>
<CAPTION>


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                              JULY  31, 1996 (UNAUDITED)
<S>                                                                                          <C>                <C>
ASSETS:
    Investments in securities, at value-Note 1(a,b).........................                                    $594,899,238
    Cash....................................................................                                       2,461,936
    Interest receivable.....................................................                                       3,695,332
    Prepaid expenses and other assets.......................................                                         141,290
                                                                                                               ______________
                                                                                                                 601,197,796
LIABILITIES:
    Due to The Dreyfus Corporation and affiliates...........................                 $273,605
    Due to Distributor......................................................                   97,190
    Accrued expenses........................................................                  164,181                534,976
                                                                                            ___________         _____________
NET ASSETS  ................................................................                                    $600,662,820
                                                                                                             ===============
REPRESENTED BY:
    Paid-in capital.........................................................                                    $600,740,750
    Accumulated net realized (loss) on investments..........................                                         (77,930)
                                                                                                               ______________
NET ASSETS at value.........................................................                                    $600,662,820
                                                                                                             ===============
Shares of Common Stock Outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                     518,383,700
                                                                                                             ===============
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                      82,357,050
                                                                                                             ===============
NET ASSET VALUE per share:
    Class A Shares
      ($518,314,105 / 518,383,700 shares)...................................                                           $1.00
                                                                                                                     =======
    Class B Shares
      ($82,348,715 / 82,357,050 shares).....................................                                          $1.00
                                                                                                                     =======







See independent accountants' review report and notes to financial
statements.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS              SIX MONTHS ENDED JULY 31, 1996 (UNAUDITED)
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                     $15,442,020
    EXPENSES:
      Management fee-Note 2(a)..............................................                    $1,406,694
      Distribution fees-Note 2(b)...........................................                        562,678
      Shareholder servicing costs-Note 2(c).................................                       178,783
      Custodian fees........................................................                        72,366
      Registration fees.....................................................                        55,110
      Professional fees.....................................................                        22,819
      Directors' fees and expenses-Note 2(d)................................                        16,343
      Prospectus and shareholders' reports..................................                        10,502
      Miscellaneous.........................................................                         5,971
                                                                                                ___________
          TOTAL EXPENSES....................................................                     2,331,266
      Less-reduction in shareholder servicing costs
          due to undertaking-Note 2(c)......................................                       29,293
                                                                                                ___________
          NET EXPENSES......................................................                                       2,301,973
                                                                                                                ____________
INVESTMENT INCOME-NET.......................................................                                      13,140,047
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                         (63,516)
                                                                                                                ____________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                     $13,076,531
                                                                                                               =============












See independent accountants' review report and notes to financial statements.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                       YEAR ENDED         SIX MONTHS ENDED
                                                                                      JANUARY 31,          JULY 31, 1996
                                                                                         1996                (UNAUDITED)
                                                                                     _______________        ______________
OPERATIONS:
    Investment income-net.............................................             $   27,392,282          $   13,140,047
    Net realized (loss) on investments................................                    (9,720)                 (63,516)
                                                                                     _______________        ______________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                27,382,562               13,076,531
                                                                                   _______________            ______________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................              (27,390,125)                (11,679,747)
      Class B shares..................................................                    (2,157)                (1,460,300)
                                                                                   _______________            ______________
          TOTAL DIVIDENDS.............................................               (27,392,282)               (13,140,047)
                                                                                   _______________            ______________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................              4,619,394,913              2,118,704,446
      Class B shares..................................................                     97,286                169,829,755
    Dividends reinvested:
      Class A shares..................................................                 26,433,785                 11,379,136
      Class B shares..................................................                     2,087                  1,458,917
    Cost of shares redeemed:
      Class A shares..................................................            (4,629,110,398)            (2,141,768,350)
      Class B shares..................................................                   (41,245)               (88,989,750)
                                                                                   _______________            ______________
          INCREASE IN NET ASSETS FROM CAPITAL
            STOCK TRANSACTIONS........................................                 16,776,428                 70,614,154
                                                                                   _______________            ______________
            TOTAL INCREASE IN NET ASSETS..............................                 16,766,708                 70,550,638
NET ASSETS:
    Beginning of year.................................................                513,345,474               530,112,182
                                                                                   _______________            ______________
    End of year.......................................................          $    530,112,182            $    600,662,820
                                                                                ================           =================








See independent accountants' review report and notes to financial statements.
</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.
<TABLE>
<CAPTION>






                                                                        CLASS A SHARES
                                               ______________________________________________________________
                                                                                                                 SIX MONTHS ENDED
                                                                     YEAR ENDED JANUARY 31,                       JULY 31, 1996
                                               ______________________________________________________________
PER SHARE DATA:                                     1992         1993         1994         1995        1996         (UNAUDITED)
                                                  ________     ________     ________     ________     ________    _____________
    <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................            .053         .033         .027        .038         .052           .023
                                                  ________     ________     ________     ________     ________        _______
    DISTRIBUTIONS;
    Dividends from investment income-net..          (.053)       (.033)       (.027)      (.038)       (.052)         (.023)
                                                  ________     ________     ________     ________     ________        _______
    Net asset value, end of period........         $  1.00      $  1.00      $  1.00     $  1.00      $  1.00         $  1.00
                                                  =========     =======     =========    =========    =========      =========
TOTAL INVESTMENT RETURN...................            5.46%       3.36%        2.69%       3.90%        5.35%         4.73%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets            .82%        .82%         .81%        .83%         .84%          .79%*
    Ratio of net investment income to average
      net assets..........................            5.27%       3.28%        2.66%       3.82%         5.22%         4.68%*
    Net Assets, end of period (000's Omitted)     $609,015     $725,419     $536,884     $513,345     $530,054       $518,314
    *Annualized.

</TABLE>









See independent accountants' review report and notes to financial statements.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS (CONTINUED)
    Contained below is per share operating performance data for a share of
Common Stock outstanding, total investment return, ratios to average net
assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.
<TABLE>
<CAPTION>

                                                                                                      CLASS B SHARES
                                                                                       __________________________________________
                                                                                            YEAR ENDED          SIX MONTHS ENDED
                                                                                            JANUARY 31,          JULY 31, 1996
PER SHARE DATA:                                                                              1996(1)              (UNAUDITED)
                                                                                          ____________           ___________
    <S>                                                                                     <C>                    <C>
    Net asset value, beginning of period..................................                  $  1.00                $  1.00
                                                                                             _______               _______
    INVESTMENT OPERATIONS;
    Investment income-net.................................................                    .042                   .022
                                                                                             _______               _______
    DISTRIBUTIONS;
    Dividends from investment income-net..................................                   (.042)                 (.022)
                                                                                             _______               _______
    Net asset value, end of period........................................                 $  1.00                 $  1.00
                                                                                          =========              ==========
TOTAL INVESTMENT RETURN...................................................                 5.04%(2)                4.53%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets...............................                 1.00%(2)                1.00%(2)
    Ratio of net investment income to average net assets..................                 5.01%(2)                4.47%(2)
    Decrease reflected in above expense ratios
      due to undertaking by the Manager...................................                  .10%(2)                 .09%(2)
    Net Assets, end of period (000's Omitted).............................                     $58                  $82,349
    (1)  From March 31, 1995 (commencement of initial offering) to January 31, 1996.
    (2)  Annualized.


</TABLE>

See independent accountants' review report and 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") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales load. The Fund offers both Class A and Class B shares. 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 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 of $1.00.
    The Fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management
estimates and assumptions. Actual results could differ from those estimates.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Directors to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Interest
income is recognized on the accrual basis. Cost of investments represents
amortized cost.
    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 custodians 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.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, if such
qualification is in the best interests of its shareholders, by complying with
the applicable provisions of the 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 $20,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to January 31, 1996. If not
applied, the carryover expires in fiscal 2004.
    At July 31, 1996, 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 for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest and extraordinary
expenses, exceed 11\2% of the average value of the Fund's net assets for any
full fiscal year. There was no expense reimbursement for the six months ended
July 31, 1996 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 of implementing and 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 securities dealer, financial
institution or other industry professional) 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.
Both the Distributor and Dreyfus determine the amounts to be paid to Service
Agents to which it will make payments and the basis on which such payments
are made. During the six months ended July 31, 1996, $497,583 was charged to
the Fund 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 six months ended July 31,
1996, $65,095 was charged to the Fund 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
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
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 six months ended July 31,
1996, the Fund was charged an aggregate of $75,401 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, 1997, that if the
aggregate expenses of Class B of the Fund (exclusive of certain expenses as
described above) 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 six
months ended July 31, 1996, $81,369 was charged to the Fund pursuant to the
Class B Shareholder Services Plan, of which $29,293 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. Such
compensation amounted to $35,125 during the six months ended July 31, 1996.
    (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.
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
    We have reviewed the accompanying statement of assets and liabilities of
General Government Securities Money Market Fund, Inc., including the
statement of investments, as of July 31, 1996, and the related statements of
operations and changes in net assets and financial highlights for the six
month period ended July 31, 1996. These financial statements and financial
highlights are the responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
January 31, 1996 and financial highlights for each of the five years in the
period ended January 31, 1996 and in our report dated March 6, 1996, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.

                              [Ernst & Young LLP signature logo]

New York, New York
September 10, 1996

[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.                        975/698SA967
[Dreyfus logo]
General Government
Securities
Money Market
Fund, Inc.
Semi-Annual Report
July 31, 1996



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