GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1995-10-11
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GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    During the last six months, U.S. economic activity declined gradually. As
might be expected, this brought about a drop in interest rates.
    As far as Government securities are concerned, other factors were at work
as well. The evident determination of the Republican Congress to reduce
Government spending, and thus hopefully cut the deficit, also had its effect
on interest rates. It is too early to tell how effective the talk of budget
cutting in Washington will be in the final analysis. However, if it should
bring about a lower level of Government borrowing, that would certainly be a
major factor in setting interest rates.
    In this environment, we are pleased that for the past six months, the
General Government Securities Money Market Fund, Inc. has produced an
annualized yield of 5.35% for Class A shares. The annualized effective yield
for Class A shares was 5.49% after compounding.* For the Fund's Class B
shares the corresponding yields were 5.04% and 5.16%.
    In managing your assets, we achieved the yield level by lengthening
maturities gradually during the six-month period. This was done in
anticipation of lower interest rates, which became more and more likely as
the economy gave continued signs of slowing down.
    The Federal Reserve Board, which raised interest rates seven times during
1994 and early 1995 to head off inflation, became concerned that the drop in
economic performance might turn into an actual business recession.
Accordingly, in early July the Federal Reserve Board reversed course and made
a modest cut in the Federal Funds rate.
    As this letter is written, the economy has cooled off from the activity
that prevailed last year. Thus, one could say that the Fed's policies have
been successful. Inflation has been held at bay and few observers believe
that the "soft landing" will turn into a full-blown economic recession.
    However, the Federal Reserve Board showed caution in the July reduction
of short-term rates. If more of that medicine is needed, we feel that the Fed
will not hesitate to act accordingly. Nonetheless, the central bank must be
ever watchful lest rate-cutting bring on the recurrence of inflation which
the Fed has so strenuously sought to avoid.
    The money markets have already discounted the possibility of further Fed
moves to lower interest rates. To a certain extent, that is already built
into current market prices. Our strategy under these circumstances is to
remain in the long end of the market as long as we believe necessary, in an
effort to seek the best possible level of yields.
    We appreciate the opportunity to put your cash to work in the money
market, and will continue to exert our best efforts to attempt to obtain
competitive returns on your behalf.
                              Sincerely,
                          [Patricia A. Larkin signature logo]
                              Patricia A. Larkin
                              Portfolio Manager
August 11, 1995
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, 1995  (UNAUDITED)
                                                                           ANNUALIZED
                                                                            YIELD ON
                                                                             DATE OF                 PRINCIPAL
U.S. GOVERNMENT AGENCIES-94.5%                                               PURCHASE                 AMOUNT         VALUE
                                                                           ------------          -------------   --------------
<S>                                                                          <C>                  <C>            <C>
Federal Farm Credit Banks, Floating Rate Notes
    11/29/95...................................................              6.19%(a)             $  25,000,000  $ 24,996,713
    9/3/96 ....................................................              6.13(a)                 50,000,000    50,000,000
    9/16/96....................................................              5.93(a)                 25,000,000    24,996,881
Federal Home Loan Banks, Discount Notes
    8/1/95.....................................................              5.75                    58,000,000    58,000,000
    1/5/96.....................................................              6.21                    25,000,000    24,351,285
    3/22/96....................................................              6.50                    15,000,000    14,404,275
Federal Home Loan Banks, Floating Rate Notes
    5/6/96.....................................................              6.07(a)                 20,000,000    19,993,589
Federal Home Loan Banks, Notes
    7/18/96....................................................              5.87                    20,000,000    20,000,000
Federal National Mortgage Association, Discount Notes
    9/11/95....................................................              6.24                    10,000,000    9,931,097
    9/15/95....................................................              6.20                    10,000,000    9,924,750
    9/25/95....................................................              5.92                    25,000,000    24,778,472
    9/28/95....................................................              6.21                    40,000,000    39,611,400
    4/19/96....................................................              5.77                    25,000,000    23,997,486
Federal National Mortgage Association, Floating Rate Notes
    6/3/96.....................................................              5.92(a)                 15,000,000    14,994,550
    10/4/96....................................................              6.20(a)                 25,000,000    25,000,000
    1/13/97....................................................              5.93(a)                 15,000,000    15,000,000
    6/20/97....................................................              5.96(a)                 20,000,000    19,996,481
    7/25/97....................................................              5.87(a)                 20,000,000    20,000,000
Student Loan Marketing Association, Floating Rate Notes
    3/20/96....................................................              5.91(b)                 17,500,000    17,500,000
    12/20/96...................................................              5.77(b)                 18,000,000    18,000,000
                                                                                                                 -------------
TOTAL U.S. GOVERNMENT AGENCIES (cost $475,476,979).............                                                   $475,476,979
                                                                                                                 =============
REPURCHASE AGREEMENTS-4.7%
Aubrey G. Lanston & Co., Inc.
    dated 7/31/95, due 8/1/95 in the amount of
    $2,000,331 (fully collateralized by
    $2,080,000 U.S. Treasury Bills due 1/4/96,
    value $2,031,909)..........................................              5.95%               $    2,000,000   $  2,000,000
Barclays De Zoete Wedd Securities, Inc.
    dated 7/31/95, due 8/1/95 in the amount of
    $20,461,268 (fully collateralized by
    $20,560,000 U.S. Treasury Notes 8.50%,
    due 11/15/95, value $21,091,040)...........................              5.75                    20,458,000    20,458,000

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                           JULY 31, 1995  (UNAUDITED)
                                                                               ANNUALIZED
                                                                               YIELD ON
                                                                                DATE OF      PRINCIPAL
REPURCHASE AGREEMENTS (CONTINUED)                                              PURCHASE        AMOUNT            VALUE
                                                                            ------------   --------------  ---------------
First Interstate Bank of California
    dated 7/31/95, due 8/1/95 in the amount of
    $1,200,179 (fully collateralized by
    $1,180,000 U.S. Treasury Notes 7.375%,
    due 5/15/96, value $1,212,827).............................              5.38%             $    1,200,000   $  1,200,000
                                                                                                                -------------
TOTAL REPURCHASE AGREEMENTS (cost $23,658,000).................                                                $  23,658,000
                                                                                                                 =============
TOTAL INVESTMENTS (cost $499,134,979)................            99.2%                                          $499,134,979
                                                                ======                                           =============
CASH AND RECEIVABLES (NET)...........................              .8%                                           $ 3,810,220
                                                                ======                                           =============
NET ASSETS...........................................            100.0%                                         $502,945,199
                                                                ======                                           =============
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, 1995 (UNAUDITED)
<S>                                                                                                 <C>           <C>
ASSETS:
    Investments in securities, at value-Note 1(a,b).........................                                      $499,134,979
    Cash....................................................................                                         2,144,770
    Interest receivable.....................................................                                         2,069,753
    Prepaid expenses........................................................                                           118,956
                                                                                                                 -------------
                                                                                                                   503,468,458
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                        $221,391
    Due to Distributor......................................................        .                103,634
    Accrued expenses........................................................        .                198,234         523,259
                                                                                                   ------------      ---------
NET ASSETS..................................................................                                      $502,945,199
                                                                                                                 =============
REPRESENTED BY:
    Paid-in capital.........................................................                                         $502,960,529
    Accumulated net realized (loss) on investments..........................                                             (15,330)
                                                                                                                 -------------
NET ASSETS at value.........................................................                                         $502,945,199
                                                                                                                 =============
Shares of Common Stock Outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                         502,881,385
                                                                                                                 =============
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                         79,144
                                                                                                                 =============
NET ASSET VALUE per share:
    Class A Shares
      ($502,866,056 / 502,881,385 shares)...................................                                         $1.00
                                                                                                                     =====
    Class B Shares
      ($79,143 / 79,144 shares).............................................                                         $1.00
                                                                                                                     =====



</TABLE>





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

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                               SIX MONTHS ENDED JULY 31, 1995 (UNAUDITED)
<S>                                                                                               <C>                <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                         $16,065,805
    EXPENSES:
      Management fee-Note 2(a)..............................................                      $1,292,502
      Distribution fees (Class A & B Shares)-Note 2(b)......................                         517,001
      Shareholder servicing costs-Note 2(c).................................                         289,981
      Custodian fees........................................................                         65,228
      Registration fees.....................................................                         47,388
      Professional fees.....................................................                         34,995
      Directors' fees and expenses-Note 2(d)................................                         18,566
      Prospectus and shareholders' reports..................................                         17,184
      Miscellaneous.........................................................                         2,673
                                                                                                ----------
                                                                                                  2,285,518
      Less-reduction of shareholder services plan costs due
          to an undertaking-Note 2(c).......................................                         55,446
                                                                                                 ----------
            TOTAL EXPENSES..................................................                                         2,230,072
                                                                                                                    -----------
INVESTMENT INCOME-NET.......................................................                                         13,835,733
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                            (10,636)
                                                                                                                    -----------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                         $13,825,097
                                                                                                                 =============








</TABLE>





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

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                          YEAR ENDED      SIX MONTHS ENDED
                                                                                          JANUARY 31,        JULY 31, 1995
                                                                                            1995              (UNAUDITED)
                                                                                  -----------------  -------------------
<S>                                                                               <C>                    <C>
OPERATIONS:
    Investment income-net.............................................            $      20,068,028      $  13,835,733
    Net realized (loss) on investments................................                      (4,571)           (10,636)
                                                                                     ---------------   ---------------
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                  20,063,457         13,825,097
                                                                                     ---------------   ---------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................                 (20,068,028)      (13,835,220)
      Class B shares..................................................                    ---                   (513)
                                                                                     ---------------   ---------------
          TOTAL DIVIDENDS.............................................                 (20,068,028)      (13,835,733)
                                                                                     ---------------   ---------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................               4,356,251,849      2,203,769,744
      Class B shares..................................................                     ---                 89,064
    Dividends reinvested:
      Class A shares..................................................                  19,433,620         13,294,715
      Class B shares..................................................                      ---                  484
    Cost of shares redeemed:
      Class A shares..................................................              (4,399,218,939)     (2,227,533,242)
      Class B shares..................................................                            ---         (10,404)
                                                                                     ---------------   ---------------
          (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS....                 (23,533,470)      (10,389,639)
                                                                                     ---------------   ---------------
            TOTAL (DECREASE) IN NET ASSETS............................                 (23,538,041)      (10,400,275)
NET ASSETS:
    Beginning of period...............................................                 536,883,515        513,345,474
                                                                                     ---------------   ---------------
    End of period.....................................................            $    513,345,474     $  502,945,199
                                                                                     ==============      =============






</TABLE>

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

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                    CLASS B SHARES
                                     ----------------------------------------------------   -------------------------------------
                                                                                             SIX MONTHS ENDED    PERIOD ENDED
                                                          YEAR ENDED JANUARY 31,               JULY 31, 1995    JULY 31, 1995
                                     ----------------------------------------------------                        (UNAUDITED)(1)
PER SHARE DATA:                       1991      1992      1993     1994            1995        (UNAUDITED)
                                    --------  --------  --------  --------       --------    --------------  -----------------
<S>                                  <C>      <C>        <C>       <C>           <C>            <C>                 <C>
    Net asset value,
      beginning of period...         $1.0000  $  .9999   $  .9999  $1.0000       $1.0000        $1.0000             $1.0000
                                    --------  --------  --------  --------       --------     --------------  -----------------
    INVESTMENT OPERATIONS:
    Investment income-net...          .0718      .0532      .0330    .0266         .0383          .0265               .0170
    Net realized gain (loss)
      on investments........          (.0001)    .-         .0001    .-            .-             .0001               .-
                                    --------  --------  --------  --------       --------     --------------  -----------------
      TOTAL FROM INVESTMENT
          OPERATIONS........           .0717     .0532      .0331    .0266          .0383         .0266               .0170
                                    --------  --------  --------  --------       --------     --------------  -----------------
    DISTRIBUTIONS:
    Dividends from investment
      income-net............          (.0718)   (.0532)   (.0330)   (.0266)      (.0383)        (.0265)              (.0170)
    Dividends from net realized
      gain on investments...           .-         .-       .-        .-           .-             .-                   .-
                                    --------  --------  --------  --------       --------     --------------  -----------------
      TOTAL DISTRIBUTIONS...         (.0718)    (.0532)   (.0330)   (.0266)      (.0383)        (.0265)             (.0170)
                                    --------  --------  --------  --------       --------     --------------  -----------------
    Net asset value, end of period  $  .9999  $  .9999   $1.0000   $1.0000       $1.0000       $1.0001             $1.0000
                                    ========  ========  ========  ========       ========     ==============  =================
TOTAL INVESTMENT RETURN.....          7.42%      5.46%     3.36%     2.69%        3.90%          5.40%(2)          5.07%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average
      net assets............           .86%       .82%      .82%      .81%         .83%            .86%(2)          1.11%(2)
    Ratio of net investment income
      to average net assets.          7.14%     5.27%      3.28%     2.66%        3.82%            5.35%(2)          5.40%(2)
    Decrease in above expense
      ratios due to undertaking
      by the Manager........           .-        .-        .-          .-          .-               .02%(2)              .-
    Net assets, end of period
      (000's Omitted).......        $408,817  $609,015  $725,419  $536,884        $513,345        $502,866              $79
(1)    From March 31, 1995 (commencement of initial offering) to July 31, 1995.
(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:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a diversified open-end management investment company. Premier Mutual Fund
Services, Inc. (the "Distributor") acts as the distributor of the Fund's
shares. The Distributor, located at One Exchange Place, Boston, Massachusetts
02109, is a wholly-owned subsidiary of FDI Distribution Services, Inc., a
provider of mutual fund administration services, which in turn is a
wholly-owned subsidiary of FDI Holdings, Inc., the parent company of which is
Boston Institutional Group, Inc. The Dreyfus Corporation ("Manager") serves
as the Fund's investment adviser. The Manager became a direct subsidiary of
Mellon Bank, N.A.
    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.
    On May 26, 1994, the Fund's Board of Directors approved an amendment to
the Fund's Charter to provide for the issuance of additional shares of the
Fund. The amendment was approved by Fund shareholders on August 3, 1994.
Pursuant to the amendment, the Fund's existing authorized shares were
classified as Class A shares and one billion newly authorized shares of
Common Stock of the Fund, par value $.01 per share, were classified as Class
B shares. The Fund began offering both Class A and Class B shares on March
31, 1995. 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.
    (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 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.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

    (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, if any, 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.
    At July 31, 1995, 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 average
daily value of the Fund's 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
on borrowings and extraordinary expenses, exceed 1 1/2% 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, 1995.
    (B) Under the Service Plan (the "Plan") with respect to Class A shares
only, 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 (a) reimburses the Distributor for payments to
certain Service Agents for distributing the Class A shares and servicing
shareholder accounts and (b) pays the Manager, Dreyfus Service Corporation, a
wholly-owned subsidiary of the Manager, or any affiliate (collectively
"Dreyfus") for servicing shareholders accounts, at an aggregate annual rate
of .20 of 1% of the value of the Fund's average daily net assets of Class A
shares. Each of the Distributor and Dreyfus may pay Service Agents (a
securities dealer, financial institution or other industry professional) a
fee in respect of the 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. Each of 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, 1995, $516,982 was charged to the Fund pursuant to the Class A Service
Plan.
    Under the Distribution Plan with respect to Class B shares ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, effective
March 31, 1995, 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 the Fund's Class B shares at an aggregate
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

annual rate of .20 of 1% of the value of the average daily net assets of
Class B shares. From March 31, 1995 through July 31, 1995, $19 was charged to
the Fund pursuant to the Class B Distribution Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan with respect to
Class A shares ("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 shares 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 six months
ended July 31, 1995, the Fund was charged an aggregate of $184,783 pursuant
to the Class A Shareholder Services Plan of which $55,446 was waived pursuant
to an undertaking by the Manager.
    Under the Shareholder Services Plan with respect to Class B shares
("Class B Shareholder Services Plan"), effective March 31, 1995, the Fund
pays the Distributor, at an annual rate of .25 of 1% of the value of the
average daily net assets of Class B shares for servicing 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. The Distributor may make payments to
service agents in respect of these services. The Distributor determines the
amounts to be paid to service agents. From March 31, 1995 through July 31,
1995, $24 was charged to Class B shares by the Distributor pursuant to the
Class B Shareholder Services Plan.
    (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, 1995, and the related statements of
operations and changes in net assets and financial highlights for the six
month period ended July 31, 1995. 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 opinio
n 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, 1995 and financial highlights for each of the five years in the
period ended January 31, 1995 and in our report dated March 6, 1995, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.
[Ernst and Young LLP signature logo]

New York, New York
September 6, 1995





[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
THE SHAREHOLDER SERVICES GROUP, INC.
P.O. Box 9671
Providence, RI 02940





Further information is contained
in the Prospectus, which must
precede or accompany this report.



Printed in U.S.A.                              975SA957
[Dreyfus logo]
GENERAL
GOVERNMENT
SECURITIES
MONEY MARKET
FUND, INC.






SEMI-ANNUAL REPORT
July 31, 1995



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