GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1994-03-23
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PRESIDENT'S LETTER

Dear Shareholder:

  As the General Government Securities Money Market Fund ended its
fiscal year on January 31, 1994, the yield was 2.66%.  After taking into
account the effect of compounding, the effective yield was 2.69%.
asterisk

  The U.S. economy is recovering from the recession at a moderate pace
as all the widely followed economic indicators have begun showing gains
in the past few weeks and months.  Industrial production, retail sales,
auto sales and sales of new and existing homes have all improved from
their recessionary lows.  The unemployment picture has been the laggard
in this recovery, but it continues to improve.

  On February 4, 1994, the apparent strength of the economy caused the
Federal Reserve Board to raise the Federal Funds rate for the first time
in five years from 3.00% to 3.25%.  While it is impossible to predict
the future, the history of the relationship between the business cycle
and short-term interest rates may provide some guidance as to possible
developments over the next year.  The cyclical decline in short-term
interest rates usually stops close to the time when a sustained economic
expansion is under way.

  Given this change in direction by the Federal Reserve Board, we will
continue to monitor closely any crosscurrents in the money markets and
seek to bring you high current income on your short-term money market
assets.

                                  Sincerely,

                                  Joseph S. DiMartino
                                  President
February 17, 1994
New York, N.Y.

asterisk Effective yield is based upon dividends declared daily and
         reinvested monthly.

<TABLE>
<CAPTION>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                               JANUARY 31, 1994

                                                                         ANNUALIZED
                                                                         YIELD ON
U.S. TREASURY BILLS--19.4%                                               DATE OF      PRINCIPAL
                                                                         PURCHASE     AMOUNT               VALUE
                                                                         ----------   ------------         ------------
<S>                                                                      <C>          <C>                  <C>

  2/10/94......................................................          3.32%        $ 30,000,000         $ 29,975,881
  3/10/94......................................................          3.36           35,000,000           34,883,193
  6/30/94......................................................          3.45           15,000,000           14,792,952
  7/28/94......................................................          3.48           25,000,000           24,586,508
                                                                                                           ------------
TOTAL U.S. TREASURY BILLS (cost $104,238,534)..................                                            $104,238,534
                                                                                                           ============
U.S. GOVERNMENT AGENCIES--81.9%

Federal Farm Credit Banks, Discount Notes
  5/31/94......................................................          3.38%        $ 10,000,000         $  9,890,256
  9/16/94......................................................          3.45            4,000,000            3,916,010
  11/2/94......................................................          3.65            4,000,000            3,892,836
Federal Farm Credit Banks, Floating Rate Notes
  10/19/94.....................................................          3.45(a)        15,000,000           15,000,000
  11/29/95.....................................................          3.44(b)        25,000,000           24,981,753
  9/3/96.......................................................          3.38(a)        50,000,000           50,000,000
Federal Home Loan Banks, Discount Notes
  5/10/94......................................................          3.44           15,000,000           14,863,208
Federal Home Loan Banks, Floating Rate Notes
  5/3/94.......................................................          3.07(b)         5,000,000            4,996,599
  11/1/94......................................................          2.72(b)        25,000,000           25,000,000
  5/6/96.......................................................          3.32(b)        20,000,000           19,981,044
  1/31/97......................................................          3.58(a)        10,000,000           10,000,000
Federal Home Loan Mortgage Corp., Discount Notes
  3/11/94......................................................          3.43            5,000,000            4,982,267
Federal National Mortgage Association, Discount Notes
  2/17/94......................................................          3.30           10,000,000            9,985,733
  3/10/94......................................................          3.32            5,000,000            4,983,299
  5/16/94......................................................          3.36           15,000,000           14,857,000
  7/11/94......................................................          3.39           20,000,000           19,704,889
  7/15/94......................................................          3.45            9,030,000            8,891,369
  9/19/94......................................................          3.40           12,000,000           11,747,894
  10/18/94.....................................................          3.40            4,880,000            4,763,790
  1/6/95.......................................................          3.52           10,300,000            9,970,228
Federal National Mortgage Association, Floating Rate Notes
  10/4/96......................................................          3.45(a)        25,000,000           25,000,000
  2/18/97......................................................          3.59(a)        20,000,000           20,000,000
Student Loan Marketing Association, Floating Rate Notes
  2/11/94......................................................          3.57(b)        25,000,000           25,000,000
  6/27/94......................................................          3.60(a)        15,000,000           15,000,000
  10/11/94.....................................................          3.40(a)        25,000,000           25,000,000
  4/24/95......................................................          3.52(b)        25,000,000           25,000,000
  6/2/95.......................................................          3.27(b)         2,500,000            2,500,000
  3/20/96......................................................          3.32(b)        17,500,000           17,500,000
Small Business Administration
Pool Certificates
  3/25/2005....................................................          4.45%(a)        1,909,960            1,909,960
  12/25/2014...................................................          4.38%(a)        2,014,234            2,007,926
  1/25/2015....................................................          4.50%(a)        1,719,541            1,719,541
  2/25/2015....................................................          4.45%(a)        4,173,236            4,173,236
  5/25/2015....................................................          4.50%(a)        2,654,406            2,654,406
                                                                                                           ------------
TOTAL U.S. GOVERNMENT AGENCIES (cost $439,873,244).............                                            $439,873,244
                                                                                                           ============
REPURCHASE AGREEMENTS--4.2%

First Interstate Bank of California
  dated 1/31/94, due 2/1/94 in the amount of $6,157,458
  (fully collateralized by $6,260,000 U.S. Treasury
  Bills due 4/7/94, value $6,226,544)..........................          2.68%         $ 6,157,000         $  6,157,000
Kidder, Peabody & Co. Inc.
  dated 1/31/94, due 2/1/94 in the amount of $16,001,378
  (fully collateralized by $16,160,000 U.S. Treasury
  Notes 4.25% due 7/31/94, value $16,313,752)..................          3.10           16,000,000           16,000,000
                                                                                                           ------------
TOTAL REPURCHASE AGREEMENTS (cost $22,157,000).................                                            $ 22,157,000
                                                                                                           ============

TOTAL INVESTMENTS (cost $566,268,778)..........          105.5%                                            $566,268,778
                                                         ======                                            ============
LIABILITIES, LESS CASH AND RECEIVABLES.........           (5.5%)                                           $(29,385,263)
                                                         ======                                            ============
NET ASSETS.....................................          100.0%                                            $536,883,515
                                                         ======                                            ============

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

<TABLE>
<CAPTION>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                    JANUARY 31, 1994
<S>                                                                                       <C>                 <C>

ASSETS:
  Investments in securities, at value--Note 1(a,b)....................................                     $566,268,778
  Cash................................................................................                          304,499
  Interest receivable.................................................................                        1,404,389
  Receivable for investment securities sold...........................................                           36,357
  Prepaid expenses....................................................................                           67,430
                                                                                                           ------------
                                                                                                            568,081,453

LIABILITIES:
  Due to The Dreyfus Corporation......................................................    $   324,299
  Payable for investment securities purchased.........................................     30,000,000
  Payable for Common Stock redeemed...................................................        692,917
  Accrued expenses....................................................................        180,722        31,197,938
                                                                                          -----------      ------------

NET ASSETS............................................................................                     $536,883,515
                                                                                                           ============

REPRESENTED BY:
  Paid-in capital.....................................................................                     $536,883,638
  Accumulated net realized (loss) on investments......................................                             (123)
                                                                                                           ------------

NET ASSETS at value applicable to 536,883,638 shares outstanding
  (15 billion shares of $.01 par value Common Stock authorized).......................                     $536,883,515
                                                                                                           ============

NET ASSET VALUE, offering and redemption price per share
  ($536,883,515 divide 536,883,638 shares)............................................                            $1.00
                                                                                                                  =====

STATEMENT OF OPERATIONS                                                                    YEAR ENDED JANUARY 31, 1994

INVESTMENT INCOME:
  INTEREST INCOME.....................................................................                     $ 21,985,860

  EXPENSES:
    Management fee--Note 2(a).........................................................    $ 3,167,232
    Shareholder servicing costs--Note 2(b,c)..........................................      1,602,202
    Custodian fees....................................................................        160,967
    Registration fees.................................................................         96,373
    Professional fees.................................................................         46,752
    Directors' fees and expenses--Note 2(d)...........................................         26,736
    Prospectus and shareholders' reports..............................................         21,379
    Miscellaneous.....................................................................         19,449
                                                                                          -----------

      TOTAL EXPENSES..................................................................                         5,141,090
                                                                                                            ------------

INVESTMENT INCOME--NET................................................................                        16,844,770
NET REALIZED GAIN ON INVESTMENTS--Note 1(b)...........................................                            20,284
                                                                                                            ------------

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..................................                      $ 16,865,054
                                                                                                            ============

</TABLE>
See notes to financial statements.
<TABLE>
<CAPTION>


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS

                                                                                              YEAR ENDED JANUARY 31,
                                                                                         ------------------------------
                                                                                             1993              1994
                                                                                         -------------    -------------
<S>                                                                                      <C>              <C>
OPERATIONS:
  Investment income--net..............................................................   $  24,153,976    $  16,844,770
  Net realized gain on investments....................................................          38,650           20,284
                                                                                         -------------    -------------
    NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..............................      24,192,626       16,865,054
                                                                                         -------------    -------------

DIVIDENDS TO SHAREHOLDERS FROM;
  Investment income--net..............................................................     (24,153,976)     (16,844,770)
                                                                                         -------------    -------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold.......................................................   6,192,301,783    4,909,502,664
  Dividends reinvested................................................................      22,179,358       15,932,788
  Cost of shares redeemed.............................................................  (6,098,116,469)  (5,113,990,985)
                                                                                         -------------    -------------

    INCREASE (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS.................     116,364,672     (188,555,533)
                                                                                         -------------    -------------

      TOTAL INCREASE (DECREASE) IN NET ASSETS.........................................     116,403,322     (188,535,249)

NET ASSETS:
  Beginning of year...................................................................     609,015,442      725,418,764
                                                                                         -------------    -------------
  End of year.........................................................................   $ 725,418,764    $ 536,883,515
                                                                                         =============    =============

See 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 year indicated. This
information has been derived from information provided in the Fund's
financial statements.
<TABLE>


                                                                                 YEAR ENDED JANUARY 31,
                                                                 ---------------------------------------------------
PER SHARE DATA:                                                    1990       1991       1992      1993        1994
                                                                 -------    -------    -------    -------    -------
<S>                                                              <C>        <C>        <C>        <C>        <C>
  Net asset value, beginning of year.....................        $1.0000    $1.0000    $ .9999    $ .9999    $1.0000
                                                                 -------    -------    -------    -------    -------

  INVESTMENT OPERATIONS:

  Investment income--net.................................          .0823      .0718      .0532      .0330      .0266
  Net realized gain (loss) on investments................          .0001     (.0001)      --        .0001       --
                                                                 -------    -------    -------    -------    -------

    TOTAL FROM INVESTMENT OPERATIONS.....................          .0824      .0717      .0532      .0331      .0266
                                                                 -------    -------    -------    -------    -------

  DISTRIBUTIONS:

  Dividends from investment income--net..................         (.0823)    (.0718)    (.0532)    (.0330)    (.0266)
  Dividends from net realized gain on investments........         (.0001)      --         --         --         --
                                                                 -------    -------    -------    -------    -------

    TOTAL DISTRIBUTIONS.................................          (.0824)    (.0718)    (.0532)    (.0330)    (.0266)
                                                                 -------    -------    -------    -------    -------

  Net asset value, end of year................................   $1.0000    $ .9999    $ .9999    $1.0000    $1.0000
                                                                 =======    =======    =======    =======    =======

TOTAL INVESTMENT RETURN.......................................      8.56%      7.42%      5.46%      3.36%      2.69%

RATIOS/SUPPLEMENTAL DATA:
  Ratio of expenses to average net assets.....................       .87%       .86%       .82%       .82%       .81%
  Ratio of net investment income to average net assets........      8.23%      7.14%      5.27%      3.28%      2.66%

  Net assets, end of year (000's Omitted)....................   $306,610   $408,817   $609,015   $725,419   $536,884
</TABLE>

See notes to financial statements.


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS

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. Dreyfus
Service Corporation ("Distributor") acts as the distributor of the
Fund's shares, which are sold to the public without a sales load. The
Distributor is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager").

  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.

  (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 custodian and,
pursuant to the terms of the repurchase agreement, must have an
aggregate market value greater than or equal to the repurchase price
plus accrued interest at all times. If the value of the underlying
securities falls below the value of the repurchase price plus accrued
interest, the Fund will require the seller to deposit additional
collateral by the next business day. If the request for additional
collateral is not met, or the seller defaults on its repurchase
obligation, the Fund maintains the right to sell the underlying
securities at market value and may claim any resulting loss against the
seller.

  (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends from investment income--net on each business day. Such
dividends are paid monthly. Dividends from net realized capital gain are
normally declared and paid annually, but the Fund may make distributions
on a more frequent basis to comply with the distribution requirements of
the Internal Revenue Code. 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 provisions
available to certain investment companies, as defined in applicable
sections of the Internal Revenue Code, and to make distributions of
taxable income sufficient to relieve it from all, or substantially all,
Federal income taxes.

  At January 31, 1994, 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, interest on
borrowings, brokerage commissions 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 year ended
January 31, 1994.

  (B) The Fund has adopted a Service Plan, pursuant to which it has
agreed to reimburse either the Manager or the Distributor for payments
made to a Service Agent (a securities dealer, financial institution, or
other industry professional), at an annual rate of .20 of 1% of the
average daily net asset value of Fund shares owned by clients of the
Service Agent. The rate and basis of such payments may be modified from
time to time by the Fund's Board of Directors. For the year ended
January 31, 1994, such reimbursement amounted to $1,267,196.

  (C) Pursuant to the Fund's Shareholder Services Plan, the Fund
reimburses the Distributor an amount not to exceed an annual rate of .25
of 1% of the value of the Fund's average daily net assets 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. During the year ended January 31, 1994, the Fund was charged
an aggregate of $126,592 pursuant to the Shareholder Services Plan.

  (C) Certain officers and directors of the Fund are "affiliated
persons," as defined in the Act, of the Manager and/or the Distributor.
Each director who is not an "affiliated person" receives an annual fee
of $2,500 and an attendance fee of $500 per meeting.

  (D) On December 5, 1993, the Manager entered into an Agreement and
Plan of Merger providing for the merger of the Manager with a subsidiary
of Mellon Bank Corporation ("Mellon").
Following the merger, it is planned that the Manager will be a direct
subsidiary of Mellon Bank, N.A. Closing of this merger is subject to a
number of contingencies, including the receipt of certain regulatory
approvals and the approvals of the stockholders of the Manager and of
Mellon. The merger is expected to occur in mid-1994, but could occur
later.

  Because the merger will constitute an "assignment" of the Fund's
Management Agreement with the Manager under the Investment Company Act
of 1940, and thus a termination of such Agreement, the Manager will seek
prior approval from the Fund's Board and shareholders.


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.

  We have audited the accompanying statement of assets and liabilities
of General Government Securities Money Market Fund, Inc., including the
statement of investments, as of January 31, 1994, and the related
statement of operations for the year then ended, the statement of
changes in net assets for each of the two years in the period then
ended, and financial highlights for each of the years indicated therein.
These financial statements and financial highlights are the
responsibility of the Fund's management. Our responsibility is to
express an opinion on these financial statements and financial
highlights based on our audits.

  We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the financial statements. Our procedures included
confirmation of securities owned as of January 31, 1994 by
correspondence with the custodians and others. An audit also includes
assessing the accounting principles used and significant estimates made
by management, as well as evaluating the overall financial statement
presentation. We believe that our audits provide a reasonable basis for
our opinion.

  In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the
financial position of General Government Securities Money Market Fund,
Inc. at January 31, 1994, the results of its operations for the year
then ended, the changes in its net assets for each of the two years in
the period then ended, and the financial highlights for each of the
indicated years, in conformity with generally accepted accounting
principles.

                                 Ernst & Young

New York, New York
March 7, 1994


GENERAL GOVERNMENT SECURITIES
MONEY MARKET FUND, INC.
144 Glenn Curtiss Boulevard
Uniondale, NY 11556

Manager
THE DREYFUS CORPORATION
200 Park Avenue, New York, NY 10166

Distributor
DREYFUS SERVICE CORPORATION
200 Park Avenue, New York, NY 10166

Custodian
THE BANK OF NEW YORK
110 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.       975AR941


GENERAL
GOVERNMENT
SECURITIES
MONEY MARKET
FUND, INC.
(G Logo)

ANNUAL REPORT
January 31, 1994








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