GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
497, 1996-06-05
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           GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
                           CLASS A AND CLASS B
                                 PART B
                   (STATEMENT OF ADDITIONAL INFORMATION)
                             JUNE 3, 1996


     This Statement of Additional Information, which is not a prospectus,
supplements and should be read in conjunction with the current Prospectus
of General Government Securities Money Market Fund, Inc. (the "Fund"),
dated June 3, 1996, as it may be revised from time to time.  To obtain a
copy of the Fund's Prospectus, please write to the Fund at 144 Glenn
Curtiss Boulevard, Uniondale, New York 11556-0144, or call the following
numbers:

               Call Toll Free 1-800-645-6561
               In New York City--Call 1-718-895-1396
               Outside the U.S. and Canada--Call 516-794-5452

     The Dreyfus Corporation (the "Manager") serves as the Fund's
investment adviser.

     Premier Mutual Fund Services, Inc. (the "Distributor") is the
distributor of the Fund's shares.

                          TABLE OF CONTENTS

                                                            Page

Investment Objective and Management Policies. . . . . . . . .B-2
Management of the Fund. . . . . . . . . . . . . . . . . . . .B-4
Management Agreement. . . . . . . . . . . . . . . . . . . . .B-7
Purchase of Shares. . . . . . . . . . . . . . . . . . . . . .B-9
Service Plan and Distribution Plan. . . . . . . . . . . . . .B-10
Shareholder Services Plans. . . . . . . . . . . . . . . . . .B-11
Redemption of Shares. . . . . . . . . . . . . . . . . . . . .B-12
Shareholder Services. . . . . . . . . . . . . . . . . . . . .B-14
Determination of Net Asset Value. . . . . . . . . . . . . . .B-18
Dividends, Distributions and Taxes. . . . . . . . . . . . . .B-19
Yield Information . . . . . . . . . . . . . . . . . . . . . .B-19
Portfolio Transactions. . . . . . . . . . . . . . . . . . . .B-20
Information About the Fund. . . . . . . . . . . . . . . . . .B-20
Transfer and Dividend Disbursing Agent, Custodian,
  Counsel and Independent Auditors. . . . . . . . . . . . . .B-20
Financial Statements. . . . . . . . . . . . . . . . . . . . .B-22
Report of Independent Auditors. . . . . . . . . . . . . . . .B-31


                 INVESTMENT OBJECTIVE AND MANAGEMENT POLICIES

     The following information supplements and should be read in
conjunction with the sections in the Fund's Prospectus entitled
"Description of the Fund" and "Appendix".

Portfolio Securities

     Repurchase Agreements.  The Fund's custodian or sub-custodian will
have custody of, and will hold in a segregated account, securities acquired
by the Fund under a repurchase agreement.  Repurchase agreements are
considered by the staff of the Securities and Exchange Commission to be
loans by the Fund.  In an attempt to reduce the risk of incurring a loss on
a repurchase agreement, the Fund will enter into repurchase agreements only
with domestic banks with total assets in excess of $1 billion, or primary
government securities dealers reporting to the Federal Reserve Bank of New
York, with respect to securities of the type in which the Fund may invest,
and will require that additional securities be deposited with it if the
value of the securities purchased should decrease below the resale price.

     Illiquid Securities.  Where a substantial market of qualified
institutional buyers develops for certain restricted securities purchased
by the Fund pursuant to Rule 144A under the Securities Act of 1933, as
amended, the Fund intends to treat such securities as liquid securities in
accordance with procedures approved by the Fund's Board.  Because it is not
possible to predict with assurance how the market for restricted securities
pursuant to Rule 144A will develop, the Fund's Board has directed the
Manager to monitor carefully the Fund's investments in such securities with
particular regard to trading activity, availability of reliable price
information and other relevant information.  To the extent that, for a
period of time, qualified institutional buyers cease purchasing restricted
securities pursuant to Rule 144A, the Fund's investing in such securities
may have the effect of increasing the level of illiquidity in the Fund's
portfolio during such period.

Investment Restrictions

     The Fund has adopted investment restrictions numbered 1 through 10 as
fundamental policies which cannot be changed without approval by the
holders of a majority (as defined in the Investment Company Act of 1940, as
amended (the "1940 Act")) of the Fund's outstanding voting shares.
Investment restrictions numbered 11 and 12 are not fundamental policies and
may be changed by vote of a majority of the Fund's Board members at any
time.  The Fund may not:

     1.   Purchase common stocks, preferred stocks, warrants or other
equity securities, or purchase corporate bonds or debentures, state bonds,
municipal bonds or industrial revenue bonds.

     2.   Borrow money, except from banks for temporary or emergency (not
leveraging) purposes in an amount up to 15% of the value of the Fund's
total assets (including the amount borrowed) based on the lesser of cost or
market, less liabilities (not including the amount borrowed) at the time
the borrowing is made.  While borrowings exceed 5% of the value of the
Fund's total assets, the Fund will not make any additional investments.

     3.   Sell securities short or purchase securities on margin.

     4.   Write or purchase put or call options.

     5.   Underwrite the securities of other issuers.

     6.   Purchase or sell real estate, real estate investment trust
securities, commodities, or oil and gas interests.

     7.   Make loans to others (except through the purchase of debt
obligations referred to under "Description of the Fund" in the Prospectus).

     8.   Invest in companies for the purpose of exercising control.

     9.   Invest in securities of other investment companies, except as
they may be acquired as part of a merger, consolidation or acquisition of
assets.

     10.  Invest more than 25% of its assets in the securities of issuers
in any industry, provided that there shall be no limitation on investments
in obligations issued or guaranteed as to principal and interest by the
U.S. Government.

     11.  Pledge, mortgage, hypothecate or otherwise encumber its assets,
except to the extent necessary to secure permitted borrowings.

     12.  Enter into repurchase agreements providing for settlement in more
than seven days after notice or purchase securities which are illiquid, if,
in the aggregate, more than 10% of the value of the Fund's net assets would
be so invested.

     If a percentage restriction is adhered to at the time of investment, a
later increase or decrease in percentage resulting from a change in values
or assets will not constitute a violation of such restriction.

     The Fund may make commitments more restrictive than the restrictions
listed above so as to permit the sale of Fund shares in certain states.
Should the Fund determine that a commitment is no longer in the best
interests of the Fund and its shareholders, the Fund reserves the right to
revoke the commitment by terminating the sale of Fund shares in the state
involved.

                          MANAGEMENT OF THE FUND

     Board members and officers of the Fund, together with information as
to their principal business occupations during at least the last five
years, are shown below.  Each Board member who is deemed to be an
"interested person" of the Fund, as defined in the 1940 Act, is indicated
by an asterisk.

Board Members of the Fund
   

CLIFFORD L. ALEXANDER, JR., Board Member.  President of Alexander &
     Associates, Inc., a management consulting firm. From 1977 to 1981, Mr.
     Alexander served as Secretary of the Army and Chairman of the Board of
     the Panama Canal Company, and from 1975 to 1977, he was a member of
     the Washington, D.C. law firm of Verner, Liipfert, Bernhard, McPherson
     and Alexander.  He is a director of American Home Products
     Corporation, The Dun & Bradstreet Corporation, MCI Communications
     Corporation, Mutual of America Life Insurance Company and TLC Beatrice
     International Holdings, Inc.  He is 62 years old and his address is
     400 C Street, N.E., Washington, D.C. 20002.
    

PEGGY C. DAVIS, Board Member.  Shad Professor of Law, New York University
     School of Law.  Professor Davis has been a member of the New York
     University law faculty since 1983.  Prior to that time, she served for
     three years as a judge in the courts of New York State; was engaged
     for eight years in the practice of law, working in both corporate and
     non-profit sectors; and served for two years as a criminal justice
     administrator in the government of the City of New York.  She writes
     and teaches in the fields of evidence, constitutional theory, family
     law, social sciences and the law, legal process and professional
     methodology and training.  She is 53 years old and her address is c/o
     New York University School of Law, 249 Sullivan Street, New York, New
     York 10012.

*JOSEPH S. DiMARTINO, Chairman of the Board.  Since January 1995, Chairman
     of the Board of various funds in the Dreyfus Family of Funds.  For
     more than five years prior thereto, he was President, a director and,
     until August 1994, Chief Operating Officer of the Manager and
     Executive Vice President and a director of Dreyfus Service
     Corporation, a wholly-owned subsidiary of the Manager and, until
     August 24, 1994, the Fund's distributor.  From August 1994 to December
     31, 1994, he was a director of Mellon Bank Corporation.  He is also
     Chairman of the Board of Directors of Noel Group, Inc., a venture
     capital company; a trustee of Bucknell University; and a director of
     the Muscular Dystrophy Association, HealthPlan Services Corporation,
     Belding Heminway, Inc., a manufacturer of industrial threads,
     specialty yarns, home furnishings and fabrics, Curtis Industries,
     Inc., a national distributor of securities products, chemicals, and
     automotive and other hardware, and Staffing Resources, Inc.  He is 52
     years old and his address is 200 Park Avenue, New York, New York
     10166.

ERNEST KAFKA, Board Member.  A physician engaged in private practice
     specializing in the psychoanalysis of adults and adolescents.  Since
     1981, he has served as an Instructor at the New York Psychoanalytic
     Institute and, prior thereto, held other teaching positions.  He is
     Associate Clinical Professor of Psychiatry at Cornell Medical School.
     For more than the past five years, Dr. Kafka has held numerous
     administrative positions and has published many articles on subjects
     in the field of psychoanalysis.  He is 63 years old and his address is
     23 East 92nd Street, New York, New York 10128.

SAUL B. KLAMAN, Board Member.  Chairman and Chief Executive Officer of SBK
     Associates, which provides research and consulting services to
     financial institutions.  Dr. Klaman was President of the National
     Association of Mutual Savings Banks until November 1983, President of
     the National Council of Savings Institutions until June 1985, Vice
     Chairman of Golembe Associates and BEI Golembe, Inc. until 1989 and
     Chairman Emeritus of BEI Golembe, Inc. until November 1992.  He also
     served as an Economist to the Board of Governors of the Federal
     Reserve System and on several Presidential Commissions, and has held
     numerous consulting and advisory positions in the fields of economics
     and housing finance.  He is 76 years old and his address is 431-B
     Dedham Street, The Gables, Newton Center, Massachusetts 02159.

NATHAN LEVENTHAL, Board Member.  President of Lincoln Center for the
     Performing Arts, Inc.  Mr. Leventhal was Deputy Mayor for Operations
     of New York City from September 1979 until March 1984 and Commissioner
     of the Department of Housing Preservation and Development of New York
     City from February 1978 to September 1979.  Mr. Leventhal was an
     associate and then a member of the New York law firm of Poletti
     Freidin Prashker Feldman and Gartner from 1974 to 1978.  He was
     Commissioner of Rent and Housing Maintenance for New York City from
     1972 to 1973.  Mr. Leventhal also serves as Chairman of Citizens
     Union, an organization which strives to reform and modernize city and
     state government.  He is 53 years old and his address is 70 Lincoln
     Center Plaza, New York, New York 10023-6583.

     For so long as the Fund's plans described in the sections captioned
"Service Plan and Distribution Plan" and "Shareholder Services Plan" remain
in effect, the Board members of the Fund who are not "interested persons"
of the Fund, as defined in the 1940 Act, will be selected and nominated by
the Board members who are not "interested persons" of the Fund.

     The Fund typically pays its Board members an annual retainer and a per
meeting fee and reimburses them for their expenses.  The Chairman of the
Board receives an additional 25% of such compensation.  Emeritus Board
members are entitled to receive an annual retainer and per meeting fee of
one-half the amount paid to them as Board members.  The aggregate amount of
compensation paid to each Board member by the Fund for the fiscal year
ended January 31, 1996, and by all other funds in the Dreyfus Family of
Funds for which such person is a Board member (the number of which is set
forth in parenthesis next to each Board member's total compensation) for
the year ended December 31, 1995, were as follows:

                                                       Total Compensation
                                     Aggregate           From Fund and
   Name of Board                 Compensation from      Fund Complex Paid
      Member                             Fund*           to Board Member

Clifford L. Alexander, Jr.              $5,500              $ 94,386 (17)

Peggy C. Davis                          $5,500              $ 81,636 (15)

Joseph S. DiMartino                     $6,875              $448,618 (94)

Ernest Kafka                            $5,500              $ 81,136 (15)

Saul B. Klaman                          $5,500              $ 81,886 (15)

Nathan Leventhal                        $5,500              $ 81,636 (15)
________________________
*    Amount does not include reimbursed expenses for attending Board meetings,
     which amounted to $297 for all Board members as a group.

Officers of the Fund

MARIE E. CONNOLLY, President and Treasurer.  President, Chief Executive
     Officer and a director of the Distributor and an officer of other
     investment companies advised or administered by the Manager.  From
     December 1991 to July 1994, she was President and Chief Compliance
     Officer of Funds Distributor, Inc., the ultimate parent of which is
     Boston Institutional Group, Inc.  Prior to December 1991, she served
     as Vice President and Controller, and later as Senior Vice President,
     of The Boston Company Advisors, Inc.  She is 38 years old.

JOHN E. PELLETIER, Vice President and Secretary.  Senior Vice President and
     General Counsel of the Distributor and an officer of other investment
     companies advised or administered by the Manager.  From February 1992
     to July 1994, he served as Counsel for The Boston Company Advisors,
     Inc.  From August 1990 to February 1992, he was employed as an
     Associate at Ropes & Gray.  He is 31 years old.

ERIC B. FISCHMAN, Vice President and Assistant Secretary.  Associate
     General Counsel of the Distributor and an officer of other investment
     companies advised or administered by the Manager.  From September 1992
     to August 1994, he was an attorney with the Board of Governors of the
     Federal Reserve System.  He is 30 years old.

ELIZABETH A. BACHMAN, Vice President and Assistant Secretary.  Assistant
     Vice President of the Distributor and an officer of other investment
     companies advised or administered by the Manager.  She is 26 years
     old.

FREDERICK C. DEY, Vice President and Assistant Treasurer.  Senior Vice
     President of the Distributor and an officer of other investment
     companies advised or administered by the Manager.  From 1988 to
     August 1994, he was manager of the High Performance Fabric Division of
     Springs Industries Inc.  He is 34 years old.

JOSEPH S. TOWER, III, Assistant Treasurer.  Senior Vice President,
     Treasurer and Chief Financial Officer of the Distributor and an
     officer of other investment companies advised or administered by the
     Manager.  From July 1988 to August 1994, he was employed by The Boston
     Company, Inc. where he held various management positions in the
     Corporate Finance and Treasury areas.  He is 33 years old.

JOHN J. PYBURN, Assistant Treasurer.  Assistant Treasurer of the
     Distributor and an officer of other investment companies advised or
     administered by the Manager.  From 1984 to July 1994, he was Assistant
     Vice President in the Mutual Fund Accounting Department of the
     Manager.  He is 60 years old.

MARGARET M. PARDO, Assistant Secretary.  Legal Assistant with the
     Distributor and an officer of other investment companies advised or
     administered by the Manager.  From June 1992 to April 1995, she was a
     Medical Coordination Officer at ORBIS International.  Prior to June
     1992, she worked as Program Coordinator at Physicians World
     Communications Group.  She is 27 years old.

     The address of each officer of the Fund is 200 Park Avenue, New York,
New York 10166.

     Board members and officers of the Fund, as a group, owned less than 1%
of the Fund's shares outstanding on May 6, 1996.


                        MANAGEMENT AGREEMENT

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Management
of the Fund."

     The Manager provides management services pursuant to the Management
Agreement (the "Agreement") dated August 24, 1994 with the Fund, which is
subject to annual approval by (i) the Fund's Board or (ii) vote of a
majority (as defined in the 1940 Act) of the outstanding voting securities
of the Fund, provided that in either event the continuance also is approved
by a majority of the Board members who are not "interested persons" (as
defined in the 1940 Act) of the Fund or the Manager, by vote cast in person
at a meeting called for the purpose of voting on such approval.  The
Agreement was approved by shareholders on August 3, 1994.  The Board,
including a majority of the Board members who are not "interested persons"
of any party to the Agreement, last voted to renew the Agreement at a
meeting held on September 27, 1995.  The Agreement is terminable without
penalty, on not more than 60 days' notice, by the Fund's Board or by vote
of the holders of a majority of the Fund's shares, or, upon not less than
90 days' notice, by the Manager.  The Agreement will terminate
automatically in the event of its assignment (as defined in the 1940 Act).
   

     The following persons are officers and/or directors of the Manager:
Howard Stein, Chairman of the Board and Chief Executive Officer; W. Keith
Smith, Vice Chairman of the Board; Christopher M. Condron, President, Chief
Operating Officer and a director; Stephen E. Canter, Vice Chairman, Chief
Investment Officer and a director; Lawrence S. Kash, Vice Chairman-
Distribution and a director; Philip L. Toia, Vice Chairman-Operations and
Administration and a director; William T. Sandalls, Jr., Senior Vice
President and Chief Financial Officer; Elie M. Genadry, Vice President-
Institutional Sales; William F. Glavin, Jr., Vice President-Corporate
Development; Mark N. Jacobs, Vice President, General Counsel and Secretary;
Patrice M. Kozlowski, Vice President-Corporate Communications; Mary Beth
Leibig, Vice President-Human Resources; Jeffrey N. Nachman, Vice President-
Mutual Fund Accounting; Andrew S. Wasser, Vice President-Information
Systems; Maurice Bendrihem, Controller; Elvira Oslapas, Assistant
Secretary; and Mandell L. Berman, Frank V. Cahouet, Alvin E. Friedman,
Lawrence M. Greene and Julian M. Smerling, directors.
    

     The Manager manages the Fund's portfolio of investments in accordance
with the stated policies of the Fund, subject to the approval of the Fund's
Board.  The Manager is responsible for investment decisions and provides
the Fund with portfolio managers who are authorized by the Board to execute
purchases and sales of securities.  The Fund's portfolio managers are
Bernard W. Kiernan and Patricia A. Larkin.  The Manager also maintains a
research department with a professional staff of portfolio managers and
securities analysts who provide research services for the Fund as well as
for other funds advised by the Manager.  All purchases and sales are
reported for the Board's review at the meeting subsequent to such
transactions.

     The Manager maintains office facilities on behalf of the Fund, and
furnishes statistical and research data, clerical help, accounting, data
processing, bookkeeping and internal auditing and certain other required
services to the Fund.  The Manager also may make such advertising and
promotional  expenditures using its own resources as it from time to time
deems appropriate.

     All expenses incurred in the operation of the Fund are borne by the
Fund, except to the extent specifically assumed by the Manager.  The
expenses borne by the Fund include:  taxes, interest, brokerage fees and
commissions, if any, fees of Board members who are not officers, directors,
employees or holders of 5% or more of the outstanding voting securities of
the Manager, Securities and Exchange Commission fees, state Blue Sky
qualification fees, charges of custodians, transfer and dividend disbursing
agents' fees, certain insurance premiums, industry association fees,
outside auditing and legal expenses, costs of maintaining the Fund's
existence, investor services (including, without limitations, telephone and
personnel expenses), cost of shareholder reports and meetings, costs of
preparing and printing prospectuses and statements of additional
information for regulatory purposes and for distribution to existing
shareholders, and any extraordinary expenses.  The Fund bears certain
expenses in accordance with separate written plans and also bears certain
costs associated with implementing and operating such plans.  See "Service
Plan and Distribution Plan."

     Under the Agreement, the Fund pays the Manager a monthly management
fee at the annual rate of .50 of 1% of the value of the Fund's average
daily net assets.  All fees and expenses are accrued daily and deducted
before payments of dividends to investors.  For the fiscal years ended
January 31, 1994, 1995 and 1996, the management fees paid by the Fund
amounted to $3,167,232, $2,624,643 and $2,622,700, respectively.

     The Manager has agreed that if in any fiscal year the aggregate
expenses of the Fund, exclusive of taxes, brokerage, interest and (with the
prior written consent of the necessary state securities commissions)
extraordinary expenses, but including the management fee, exceed 1-1/2% of
the average value of the Fund's net assets for that fiscal year, the Fund may
deduct from the payment to be made to the Manager under the Agreement, or
the Manager will bear, such excess expense.  Such deduction or payment, if
any, will be estimated daily and reconciled and effected or paid, as the
case may be, on a monthly basis.  No such deduction or payment was required
for the fiscal year ended January 31, 1996.

     The aggregate of the fees paid to the Manager is not subject to
reduction as the value of the Fund's net assets increases.


                        PURCHASE OF SHARES

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "How to Buy
Shares."

     The Distributor.  The Distributor serves as the Fund's distributor on
a best efforts basis pursuant to an agreement which is renewable annually.
The Distributor also acts as distributor for the other funds in the Dreyfus
Family of Funds and for certain other investment companies.  In some
states, certain financial institutions effecting transactions in Fund
shares may be required to register as dealers pursuant to state law.

     Using Federal Funds.  Dreyfus Transfer, Inc., the Fund's transfer and
dividend disbursing agent (the "Transfer Agent"), or the Fund may attempt
to notify the investor upon receipt of checks drawn on banks that are not
members of the Federal Reserve System as to the possible delay in
conversion into Federal Funds and may attempt to arrange for a better means
of transmitting the money.  If the investor is a customer of a securities
dealer ("Selected Dealer") and his order to purchase Fund shares is paid
for other than in Federal Funds, the Selected Dealer, acting on behalf of
its customer, will complete the conversion into, or itself advance, Federal
Funds generally on the business day following receipt of the customer
order.  The order is effective only when so converted and received by the
Transfer Agent.  An order for the purchase of Fund shares placed by an
investor with sufficient Federal Funds or a cash balance in his brokerage
account with a Selected Dealer will become effective on the day that the
order, including Federal Funds, is received by the Transfer Agent.

     Reopening an Account.  An investor may reopen an account with a
minimum investment of $100 without filing a new Account Application during
the calendar year the account is closed or during the following calendar
year, provided the information on the old Account Application is still
applicable.


                   SERVICE PLAN AND DISTRIBUTION PLAN

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Service
Plan and Distribution Plan."

     Rule 12b-1 (the "Rule") adopted by the Securities and Exchange
Commission under the 1940 Act provides, among other things, that an
investment company may bear expenses of distributing its shares only
pursuant to a plan adopted in accordance with the Rule.  The Fund's Board
has adopted such a plan with respect to Class A and Class B (each, a
"Plan").  Under each Plan, the Fund bears directly the costs of preparing,
printing and distributing prospectuses and statements of additional
information and of implementing and operating the Plan.  Under the Plan
adopted with respect to Class A (the "Service Plan"), the Fund reimburses
(a) the Distributor for payments made for distributing the Class A shares
and servicing shareholder accounts ("Servicing") and (b) the Manager,
Dreyfus Service Corporation and any affiliate of either of them
(collectively, "Dreyfus") for payments made for Servicing.  Each of the
Distributor and Dreyfus may pay one or more financial institutions,
Selected Dealers or other industry professionals (collectively, "Service
Agents") a fee in respect of Class A shares owned by shareholders with whom
the Service Agent has a Servicing relationship or for whom the Service
Agent is the dealer or holder of record.  Under the Plan adopted with
respect to Class B (the "Distribution Plan"), the Fund reimburses the
Distributor for payments made to third parties for distributing (within the
meaning of the Rule) Class B shares.  The Fund's Board believes that there
is a reasonable likelihood that each Plan will benefit the Fund and holders
of the relevant Class of shares.

     A quarterly report of the amounts expended under each Plan, and the
purposes for which such expenditures were incurred, must be made to the
Fund's Board for its review.  In addition, each Plan provides that it may
not be amended to increase materially the costs which the Fund may bear for
distribution pursuant to the Plan without shareholder approval of the
affected Class and that other material amendments of the Plan must be
approved by the Board, and by the Board members who are not "interested
persons" (as defined in the 1940 Act) of the Fund or the Manager and have
no direct or indirect financial interest in the operation of the Plan or in
any related agreements entered into in connection with such Plan, by vote
cast in person at a meeting called for the purpose of considering such
amendments.  Each Plan is subject to annual approval by such vote of the
Board members cast in person at a meeting called for the purpose of voting
on the Plan.  Each Plan was last so approved at a meeting held on September
27, 1995.  Each Plan is terminable at any time by vote of a majority of the
Board members who are not "interested persons" and have no direct or
indirect financial interest in the operation of the Plan or in any of the
related agreements or by vote of a majority of the relevant Class of
shares.

     For the fiscal year ended January 31, 1996, the Distributor paid
$1,856,688 to Service Agents for Servicing, of which $1,048,994 was
reimbursed by the Fund pursuant to the Service Plan and the Manager
reimbursed the remainder.  In addition, for the fiscal year ended January
31, 1996, the Fund paid $25,084 for preparing, printing and distributing
prospectuses and statements of additional information and for implementing
and operating the Service Plan.

     For the period March 31, 1995 (effective date of the Distribution
Plan) through January 31, 1996, the Fund paid the Distributor $86 with
respect to Class B under the Distribution Plan.


                       SHAREHOLDER SERVICES PLANS

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Shareholder
Services Plans."

     The Fund has adopted a Shareholder Services Plan with respect to Class
A pursuant to which the Fund reimburses Dreyfus Service Corporation for
certain allocated expenses of providing personal services and/or
maintaining shareholder accounts.  The Fund also has adopted a Shareholder
Services Plan with respect to Class B pursuant to which the Fund pays the
Distributor for the provision of certain services to the holders of Class B
shares.  Under each Shareholder Services Plan, 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.  Under the Shareholder Services Plan for Class B, the
Distributor may make payments to Service Agents in respect of these
services.

     A quarterly report of the amounts expended under each Shareholder
Services Plan, and the purposes for which such expenditures were incurred,
must be made to the Fund's Board for its review.  In addition, each
Shareholder Services Plan provides that material amendments of the
Shareholder Services Plan must be approved by the Fund's Board, and by the
Board members who are not "interested persons" (as defined in the 1940 Act)
of the Fund and have no direct or indirect financial interest in the
operation of the Shareholder Services Plan by vote cast in person at a
meeting called for the purpose of considering such amendments.  Each
Shareholder Services Plan is subject to annual approval by such vote of the
Board members cast in person at a meeting called for the purpose of voting
on the Shareholder Services Plan.  Each Shareholder Services Plan was last
so approved on September 27, 1995.  Each Shareholder Services Plan is
terminable at any time by vote of a majority of the Board members who are
not "interested persons" and have no direct or indirect financial interest
in the operation of the Shareholder Services Plan.

     For the fiscal year ended January 31, 1996, the Fund was charged
$229,788 pursuant to the Shareholder Services Plan with respect to Class A.

     For the period March 31, 1995 (effective date of the Shareholder
Services Plan for Class B) through January 31, 1996, the Fund was charged
$108 pursuant to the Shareholder Services Plan with respect to Class B, of
which $43 was reimbursed by the Manager pursuant to an undertaking.


                         REDEMPTION OF SHARES

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "How to
Redeem Shares."

     Check Redemption Privilege.  An investor may indicate on the Account
Application, Shareholder Services Form or by later written request that the
Fund provide Redemption Checks ("Checks") drawn on the investor's Fund
account.  Checks will be sent only to the registered owner(s) of the
account and only to the address of record.  The Account Application,
Shareholder Services Form or later written request must be manually signed
by the registered owner(s).  Checks may be made payable to the order of any
person in an amount of $500 or more.  When a Check is presented to the
Transfer Agent for payment, the Transfer Agent, as the investor's agent,
will cause the Fund to redeem a sufficient number of shares in the
investor's account to cover the amount of the Check.  Dividends are earned
until the Check clears.  After clearance, a copy of the Check will be
returned to the investor.  Investors generally will be subject to the same
rules and regulations that apply to checking accounts, although election of
this Privilege creates only a shareholder-transfer agent relationship with
the Transfer Agent.

     If the amount of the Check is greater than the value of the shares in
an investor's account, the Check will be returned marked insufficient
funds.  Checks should not be used to close an account.

     Wire Redemption Privilege.  By using this Privilege, the investor
authorizes the Transfer Agent to act on wire or telephone redemption
instructions from any person representing himself or herself to be the
investor or a representative of the investor's Service Agent, and
reasonably believed by the Transfer Agent to be genuine.  The Transfer
Agent's records of such instructions are binding.  Ordinarily, the Fund
will initiate payment for shares redeemed pursuant to this Privilege on the
same business day if the Transfer Agent receives the redemption request in
proper form prior to 12:00 Noon, New York time, on such day; otherwise, the
Fund will initiate payment on the next business day.  Redemption proceeds
($1,000 minimum) will be transferred by Federal Reserve wire only to the
commercial bank account specified by the investor on the Account
Application or Shareholder Services Form, or to a correspondent bank if the
investor's bank is not a member of the Federal Reserve System.  Fees
ordinarily are imposed by such bank and usually are borne by the investor.
Immediate notification by the correspondent bank to the investor's bank is
necessary to avoid a delay in crediting the funds to the investor's bank
account.

     Investors with access to telegraphic equipment may wire redemption
requests to the Transfer Agent by employing the following transmittal code
which may be used for domestic or overseas transmissions:

                                   Transfer Agent's
          Transmittal Code              Answer Back Sign

               144295              144295 TSSG PREP

     Investors who do not have direct access to telegraphic equipment may
have the wire transmitted by contacting a TRT Cables operator at
1-800-654-7171, toll free.  Investors should advise the operator that the
above transmittal code must be used and should also inform the operator of
the Transfer Agent's answer back sign.

     To change the commercial bank or account designated to receive
redemption proceeds, a written request must be sent to the Transfer Agent.
This request must be signed by each shareholder, with each signature
guaranteed as described below under "Stock Certificates; Signatures."

     Stock Certificates; Signatures.  Any certificates representing Fund
shares to be redeemed must be submitted with the redemption request.
Written redemption requests must be signed by each shareholder, including
each holder of a joint account, and each signature must be guaranteed.
Signatures on endorsed certificates submitted for redemption also must be
guaranteed.  The Transfer Agent has adopted standards and procedures
pursuant to which signature-guarantees in proper form generally will be
accepted from domestic banks, brokers, dealers, credit unions, national
securities exchanges, registered securities associations,  clearing
agencies and savings associations, as well as from participants in the New
York Stock Exchange Medallion Signature Program, the Securities Transfer
Agents Medallion Program ("STAMP"), and the Stock Exchanges Medallion
Program.  Guarantees must be signed by an authorized signatory of the
guarantor and "Signature-Guaranteed" must appear with the signature.  The
Transfer Agent may request additional documentation from corporations,
executors, administrators, trustees or guardians, and may accept other
suitable verification arrangements from foreign investors, such as consular
verification.  For more information with respect to signature-guarantees,
please call one of the telephone numbers listed on the cover.

     Redemption Commitment.  The Fund has committed itself to pay in cash
all redemption requests by any shareholder of record, limited in amount
during any 90-day period to the lesser of $250,000 or 1% of the value of
the Fund's net assets at the beginning of such period.  Such commitment is
irrevocable without the prior approval of the Securities and Exchange
Commission.  In the case of requests for redemption in excess of such
amount, the Fund's Board reserves the right to make payments in whole or in
part in securities or other assets of the Fund in case of an emergency or
any time a cash distribution would impair the liquidity of the Fund to the
detriment of the existing shareholders.  In such event, the securities
would be valued in the same manner as the Fund's portfolio is valued.  If
the recipient sold such securities, brokerage charges would be incurred.

     Suspension of Redemptions.  The right of redemption may be suspended
or the date of payment postponed (a) during any period when the New York
Stock Exchange is closed (other than customary weekend and holiday
closings), (b) when trading in the markets the Fund ordinarily utilizes is
restricted, or when an emergency exists as determined by the Securities and
Exchange Commission so that disposal of the Fund's investments or
determination of its net asset value is not reasonably practicable, or (c)
for such other periods as the Securities and Exchange Commission by order
may permit to protect the Fund's shareholders.


                        SHAREHOLDER SERVICES

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Shareholder
Services."

     Fund Exchanges.  Shares of other funds purchased by exchange will be
purchased on the basis of relative net asset value per share as follows:

     A.  Exchanges for shares of funds that are offered without a sales
         load will be made without a sales load.

     B.  Shares of funds purchased without a sales load may be exchanged
         for Shares of other funds sold with a sales load, and the
         applicable sales load will be deducted.

     C.  Shares of funds purchased with a sales load may be exchanged
         without a sales load for shares of other funds sold without a
         sales load.

     D.  Shares of funds purchased with a sales load, shares of funds
         acquired by a previous exchange from shares purchased with a sales
         load, and additional shares acquired through reinvestment of
         dividends or distributions of any such funds (collectively
         referred to herein as "Purchased Shares") may be exchanged for
         shares of other funds sold with a sales load (referred to herein
         as "Offered Shares"), provided that, if the sales load applicable
         to the Offered Shares exceeds the maximum sales load that could
         have been imposed in connection with the Purchased Shares (at the
         time the Purchased Shares were acquired), without giving effect to
         any reduced loads, the difference will be deducted.

     To accomplish an exchange under item D above, shareholders must notify
the Transfer Agent of their prior ownership of fund shares and their
account numbers.

     To request an exchange, an investor, or the investor's Service Agent
acting on the investor's behalf, must give exchange instructions to the
Transfer Agent in writing or by telephone.  The ability to issue exchange
instructions by telephone is given to all Fund shareholders automatically,
unless the investor checks the applicable "No" box on the Account
Application, indicating that the investor specifically refuses this
Privilege.  By using the Telephone Exchange Privilege, the investor
authorizes the Transfer Agent to act on telephonic instructions from any
person representing himself or herself to be the investor or a
representative of the investor's Service Agent, and reasonably believed by
the Transfer Agent to be genuine.  Telephone exchanges may be subject to
the limitations as to the amount involved or the number of telephone
exchanges permitted.  Shares issued in certificate form are not eligible
for telephone exchange.

     To establish a personal retirement plan by exchange, shares of the
fund being exchanged must have a value of at least the minimum initial
investment required for the fund into which the exchange is being made.
For Dreyfus-sponsored Keogh Plans, IRAs and IRAs set up under a Simplified
Employee Pension Plan ("SEP-IRAs") with only one participant, the minimum
initial investment is $750.  To exchange shares held in corporate plans,
403(b)(7) Plans and SEP-IRAs with more than one participant, the minimum
initial investment is $100 if the plan has at least $2,500 invested among
the funds in the Dreyfus Family of Funds.  To exchange shares held in
personal retirement plans, the shares exchanged must have a current value
of at least $100.

     Auto-Exchange Privilege.  The Auto-Exchange Privilege permits an
investor to purchase, in exchange for shares of the Fund, shares of another
fund in the Dreyfus Family of Funds.  This Privilege is available only for
existing accounts.  Shares will be exchanged on the basis of relative net
asset value as described above under "Fund Exchanges."  Enrollment in or
modification or cancellation of this Privilege is effective three business
days following notification by the investor.  An investor will be notified
if his account falls below the amount designated to be exchanged under this
Privilege.  In this case, an investor's account will fall to zero unless
additional investments are made in excess of the designated amount prior to
the next Auto-Exchange transaction.  Shares held under IRA and other
retirement plans are eligible for this Privilege.  Exchanges of IRA shares
may be made between IRA accounts and from regular accounts to IRA accounts,
but not from IRA accounts to regular accounts.  With respect to all other
retirement accounts, exchanges may be made only among those accounts.

     Fund Exchanges and the Auto-Exchange Privilege are available to
shareholders resident in any state in which shares of the fund being
acquired legally may be sold.  Shares may be exchanged only between
accounts having identical names and other identifying designations.

     Shareholder Services Forms and prospectuses of other funds may be
obtained by calling 1-800-645-6561.  The Fund reserves the right to reject
any exchange request in whole or in part.  The Fund Exchanges service or
the Auto-Exchange Privilege may be modified or terminated at any time upon
notice to shareholders.

     Automatic Withdrawal Plan.  The Automatic Withdrawal Plan permits an
investor with a $5,000 minimum account to request withdrawal of a specified
dollar amount (minimum of $50) on either a monthly or quarterly basis.
Withdrawal payments are the proceeds from sales of Fund shares, not the
yield on the shares.  If withdrawal payments exceed reinvested dividends
and distributions, the investor's shares will be reduced and eventually may
be depleted.  Automatic Withdrawal may be terminated at any time by the
investor, the Fund or the Transfer Agent.  Shares for which certificates
have been issued may not be redeemed through the Automatic Withdrawal Plan.


     Dividend Sweep.  Dividend Sweep allows investors to invest on the
payment date their dividends or dividends and capital gain distributions,
if any, from the Fund in shares of another fund in the Dreyfus Family of
Funds of which the investor is a shareholder.  Shares of other funds
purchased pursuant to this privilege will be purchased on the basis of
relative net asset value per share as follows:

     A.  Dividends and distributions paid by a fund may be invested without
         imposition of a sales load in shares of other funds that are
         offered without a sales load.

     B.  Dividends and distributions paid by a fund which does not charge a
         sales load may be invested in shares of other funds sold with a
         sales load, and the applicable sales load will be deducted.

     C.  Dividends and distributions paid by a fund which charges a sales
         load may be invested in shares of other funds sold with a sales
         load (referred to herein as "Offered Shares"), provided that, if
         the sales load applicable to the Offered Shares exceeds the
         maximum sales load charged by the fund from which dividends or
         distributions are being swept, without giving effect to any
         reduced loads, the difference will be deducted.

     D.  Dividends and distributions paid by a fund may be invested in
         shares of other funds that impose a contingent deferred sales
         charge ("CDSC") and the applicable CDSC, if any, will be imposed
         upon redemption of such shares.

     Corporate Pension/Profit-Sharing and Personal Retirement Plans.  The
Fund makes available to corporations a variety of prototype pension and
profit-sharing plans, including a 401(k) Salary Reduction Plan.  In
addition, the Fund makes available Keogh Plans, IRAs, including SEP-IRAs
and IRA "Rollover Accounts," and 403(b)(7) Plans.  Plan support services
also are available.  Investors can obtain details on the various plans by
calling the following numbers toll free:  for Keogh Plans, please call 1-
800-358-5566; for IRAs and IRA "Rollover Accounts," please call 1-800-645-
6561; or for SEP-IRAs, 401(k) Salary Reduction Plans and for 403(b)(7)
Plans, please call 1-800-322-7880.

     Investors who wish to purchase Fund shares in conjunction with a Keogh
Plan, a 403(b)(7) Plan or an IRA, including a SEP-IRA, may request from the
Distributor forms for adoption of such plans.

     The entity acting as a custodian for Keogh Plans, 403(b)(7) Plans or
IRAs may charge a fee, payment of which could require the liquidation of
shares.  All fees charged are described in the appropriate form.

     Shares may be purchased in connection with these plans only by direct
remittance to the entity which acts as custodian.  Such purchases will be
effective when payments received by the Transfer Agent are converted into
Federal Funds.  Purchases for these plans may not be made in advance of
receipt of Federal Funds.

     The minimum initial investment for corporate plans, salary reduction
plans, 403(b)(7) Plans and SEP-IRAs, with more than one participant, is
$2,500, with no minimum on subsequent purchases.  The minimum initial
investment for Dreyfus-sponsored Keogh Plans, IRAs, SEP-IRAs and 403(b)(7)
Plans, with only one participant, is normally $750, with no minimum on
subsequent purchases.  Individuals who open an IRA also may open a
non-working spousal IRA with a minimum investment of $250.

     The investor should read the prototype retirement plans and the
applicable form of custodial agreement for further details as to
eligibility, service fees and tax implications, and should consult a tax
adviser.

                   DETERMINATION OF NET ASSET VALUE

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "How to Buy
Shares."

     Amortized Cost Pricing.  The valuation of the Fund's portfolio
securities is based upon their amortized cost, which does not take into
account unrealized capital gains or losses.  This involves valuing an
instrument at its cost and thereafter assuming a constant amortization to
maturity of any discount or premium, regardless of the impact of
fluctuating interest rates on the market value of the instrument.  While
this method provides certainty in valuation, it may result in periods
during which value, as determined by amortized cost, is higher or lower
than the price the Fund would receive if it sold the instrument.

     The Fund's Board has established, as a particular responsibility
within the overall duty of care owed to the Fund's investors, procedures
reasonably designed to stabilize the Fund's price per share as computed for
the purpose of purchases and redemptions at $1.00.  Such procedures include
review of the Fund's portfolio holdings by the Board, at such intervals as
it may deem appropriate, to determine whether the Fund's net asset value
calculated by using available market quotations or market equivalents
deviates from $1.00 per share based on amortized cost.  In such review,
investments for which market quotations are readily available will be
valued at the most recent bid price or yield equivalent for such securities
of comparable maturity, quality and type as obtained from one or more of
the major market makers for the securities to be valued.  Other investments
and assets will be valued at fair value as determined in good faith by the
Board.

     The extent of any deviation between the Fund's net asset value based
upon available market quotations or market equivalents and $1.00 per share
based on amortized cost will be examined by the Fund's Board.  If such
deviation exceeds 1/2 of 1%, the Board promptly will consider what action,
if any, will be initiated.  In the event the Board determines that a
deviation exists which may result in material dilution or other unfair
results to investors or existing shareholders, it has agreed to take such
corrective action as it regards as necessary and appropriate, including:
selling portfolio instruments prior to maturity to realize capital gains or
losses or to shorten average portfolio maturity; withholding dividends or
paying distributions from capital or capital gains; redeeming shares in
kind; or establishing a net asset value per share by using available market
quotations or market equivalents.

     New York Stock Exchange Closings.  The holidays (as observed) on which
the New York Stock Exchange is closed currently are:  New Year's Day,
Presidents' Day, Good Friday, Memorial Day, Independence Day, Labor Day,
Thanksgiving and Christmas.

                  DIVIDENDS, DISTRIBUTIONS AND TAXES

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Dividends,
Distributions and Taxes."

     Ordinarily, gains and losses realized from portfolio transactions will
be treated as capital gain or loss.  However, all or a portion of any gains
realized from the sale or other disposition of certain market discount
bonds will be treated as ordinary income under Section 1276 of the Internal
Revenue Code of 1986, as amended.


                          YIELD INFORMATION

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "Yield
Information."

     For the seven-day period ended January 31, 1996, the Fund's yield was
4.90% for Class A and 4.72% for Class B and the Fund's effective yield was
5.02% for Class A and 4.83% for Class B.  The yield for Class B reflects
the reimbursement of certain expenses attributable to Class B, without
which the Fund's Class B yield and the effective yield for the seven-day
period ended January 31, 1996 would have been 4.62% and 4.73%,
respectively.  Yield is computed in accordance with a standardized method
which involves determining the net change in the value of a hypothetical
pre-existing Fund account having a balance of one share at the beginning of
a seven calendar day period for which yield is to be quoted, dividing the
net change by the value of the account at the beginning of the period to
obtain the base period return, and annualizing the results (i.e.,
multiplying the base period return by 365/7).  The net change in the value
of the account reflects the value of additional shares purchased with
dividends declared on the original share and any such additional shares and
fees that may be charged to shareholder accounts, in proportion to the
length of the base period and the Fund's average account size, but does not
include realized gains and losses or unrealized appreciation and
depreciation.  Effective yield is computed by adding 1 to the base period
return (calculated as described above), raising that sum to a power equal
to 365 divided by 7, and subtracting 1 from the result.

     Yields will fluctuate and are not necessarily representative of future
results.  Each investor should remember that yield is a function of the
type and quality of the instruments in the portfolio, portfolio maturity
and operating expenses.  An investor's principal in the Fund is not
guaranteed.  See "Determination of Net Asset Value" for a discussion of the
manner in which the Fund's price per share is determined.

                      PORTFOLIO TRANSACTIONS

     Portfolio securities ordinarily are purchased directly from the issuer
or from an underwriter or a market maker for the securities.  Usually no
brokerage commissions are paid by the Fund for such purchases.  Purchases
from underwriters of portfolio securities include a concession paid by the
issuer to the underwriter and the purchase price paid to market makers for
the securities may include the spread between the bid and asked price.  No
brokerage commissions have been paid by the Fund to date.

     Transactions are allocated to various dealers by the Fund's portfolio
managers in their best judgment.  The primary consideration is prompt and
effective execution of orders at the most favorable price.  Subject to that
primary consideration, dealers may be selected for research, statistical or
other services to enable the Manager to supplement its own research and
analysis with the views and information of other securities firms and may
be selected based upon their sales of Fund shares.

     Research services furnished by brokers through which the Fund effects
securities transactions may be used by the Manager in advising other funds
it advises and, conversely, research services furnished to the Manager by
brokers in connection with other funds the Manager advises may be used by
the Manager in advising the Fund.  Although it is not possible to place a
dollar value on these services, it is the opinion of the Manager that the
receipt and study of such services should not reduce the overall expenses
of its research department.


                     INFORMATION ABOUT THE FUND

     The following information supplements and should be read in
conjunction with the section in the Fund's Prospectus entitled "General
Information."

     Each Fund share has one vote and, when issued and paid for in
accordance with the terms of the offering, is fully paid and
non-assessable.  Fund shares have equal rights as to dividends and in
liquidation.  Shares have no preemptive, subscription or conversion rights
and are freely transferable.

     The Fund sends annual and semi-annual financial statements to all its
shareholders.


            TRANSFER AND DIVIDEND DISBURSING AGENT, CUSTODIAN,
                  COUNSEL AND INDEPENDENT AUDITORS

     Dreyfus Transfer, Inc., a wholly-owned subsidiary of the Manager, P.O.
Box 9671, Providence, Rhode Island 02940-9671, is the Fund's transfer and
dividend disbursing agent.  Under a transfer agency agreement with the
Fund, the Transfer Agent arranges for the maintenance of shareholder
account records for the Fund, the handling of certain communications
between shareholders and the Fund and the payment of dividends and
distributions payable by the Fund.  For these services, the Transfer Agent
receives a monthly fee computed on the basis of the number of shareholder
accounts it maintains for the Fund during the month, and is reimbursed for
certain out-of-pocket expenses.  For the period December 1, 1995 (effective
date of transfer agency agreement) through January 31, 1996, the Fund paid
the Transfer Agent $11,715.

     The Bank of New York, 90 Washington Street, New York, New York 10286,
is the Fund's custodian.

     First Interstate Bank of California, 707 Wilshire Boulevard, Los
Angeles, California 90017, serves as a sub-custodian of the Fund's
investments.

     The Transfer Agent, The Bank of New York and First Interstate Bank of
California have no part in determining the investment policies of the Fund
or which securities are to be purchased or sold by the Fund.

     Stroock & Stroock & Lavan, 7 Hanover Square, New York, New York
10004-2696, as counsel for the Fund, has rendered its opinion as to certain
legal matters regarding the due authorization and valid issuance of the
shares being sold pursuant to the Fund's Prospectus.

     Ernst & Young LLP, 787 Seventh Avenue, New York, New York 10019,
independent auditors, have been selected as auditors of the Fund.

 
<TABLE>
<CAPTION>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                              JANUARY 31, 1996
                                                                          ANNUALIZED
                                                                           YIELD ON
                                                                             DATE OF                  PRINCIPAL
U.S. TREASURY BILLS-6.4%                                                    PURCHASE                   AMOUNT          VALUE
                                                                             ______                    _______        _______
    <S>                                                                      <C>                 <C>             <C>
    8/22/96
      (cost $33,918,461).......................................              5.80%               $  35,000,000   $ 33,918,461
                                                                                                                      =======
U.S. GOVERNMENT AGENCIES-90.1%
Federal Farm Credit Banks, Floating Rate Notes
    9/3/96.....................................................              5.88 (a)             $  50,000,000  $ 50,000,000
    9/16/96....................................................              5.68 (a)                25,000,000    24,998,274
    11/7/96....................................................              5.58 (a)                15,000,000    14,988,931
    7/25/97....................................................              5.58 (a)                15,000,000    14,991,518
    9/15/97....................................................              5.63 (a)                15,000,000    14,988,618
Federal Home Loan Banks, Discount Notes
    2/1/96.....................................................              5.75                    30,000,000    30,000,000
    3/22/96....................................................              6.50                    15,000,000    14,872,708
    11/7/96....................................................              5.46                    15,000,000    14,997,753
    11/20/96...................................................              5.47                    10,000,000    9,990,484
Federal Home Loan Banks, Floating Rate Notes
    5/6/96.....................................................              5.82 (a)                20,000,000    19,997,817
    1/26/98....................................................              5.74 (a)                4,000,000      4,007,073
Federal National Mortgage Association, Discount Notes
    4/18/96....................................................              5.24                    15,140,000    14,972,257
    4/19/96....................................................              5.77                    25,000,000    24,701,542
    7/12/96....................................................              5.11                    25,000,000    24,438,625
    9/18/96....................................................              5.31                    20,000,000    19,347,056
Federal National Mortgage Association, Floating Rate Notes
    6/3/96.....................................................              5.67 (a)                15,000,000    14,997,817
    10/4/96....................................................              5.95 (a)                25,000,000    25,000,000
    12/16/96...................................................              5.56 (a)                10,000,000    9,991,533
    1/13/97....................................................              5.68 (a)                15,000,000    15,000,000
    6/20/97....................................................              5.71 (a)                20,000,000    19,997,420
    7/25/97....................................................              5.62 (a)                20,000,000    20,000,000
    8/18/97....................................................              5.63 (a)                30,000,000    29,993,056
    1/21/98....................................................              5.61 (a)                10,000,000    9,989,827
Student Loan Marketing Association, Floating Rate Notes
    3/20/96....................................................              5.42 (b)                17,500,000    17,500,000
    12/20/96...................................................              5.28 (b)                18,000,000    17,999,996
                                                                                                                      _______
TOTAL U.S. GOVERNMENT AGENCIES (cost $477,762,305).............                                                  $477,762,305
                                                                                                                      =======

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                     JANUARY 31, 1996
                                                                             ANNUALIZED
                                                                             YIELD ON
                                                                             DATE OF                  PRINCIPAL
REPURCHASE AGREEMENTS-3.1%                                                   PURCHASE                   AMOUNT        VALUE
                                                                             ______                     _______       _______

First Interstate Bank of California
    dated 1/31/96, due 2/1/96 in the amount of
    $1,789,273 (fully collateralized by
    $1,771,000 U.S. Treasury Notes 7.375%,
    due 5/15/96, value $1,810,416).............................              5.50%               $    1,789,000  $  1,789,000
Lehman Government Securities, Inc.
    dated 1/31/96, due 2/1/96 in the amount of
    $10,001,639 (fully collateralized by
    $10,145,000 U.S. Treasury Notes 6.125%,
    due 7/31/96, value $10,197,432)............................              5.90                    10,000,000    10,000,000
SBC Capital Markets
    dated 1/31/96, due 2/1/96 in the amount of
    $4,500,688 (fully collateralized by
    $4,740,000 U.S. Treasury Bills,
    due 9/19/96, value $4,569,760).............................              5.50                    4,500,000      4,500,000
                                                                                                                      ______-
TOTAL REPURCHASE AGREEMENTS (cost $16,289,000).................                                                  $ 16,289,000
                                                                                                                      =======
TOTAL INVESTMENTS (cost $527,969,766)..............            99.6%                                             $527,969,766
                                                               ====                                                   =======
CASH AND RECEIVABLES (NET).........................      .      .4%                                              $  2,142,416
                                                               ====                                                   =======
NET ASSETS.........................................          100.0%                                              $530,112,182
                                                               ====                                                   =======

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.





See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                     JANUARY 31, 1996
<S>                                                                                                <C>         <C>
ASSETS:
    Investments in securities, at value-Note 1(a,b).........................                                   $527,969,766
    Interest receivable.....................................................                                      2,706,553
    Prepaid expenses and other assets.......................................                                         60,671
                                                                                                                    _______
                                                                                                                530,736,990
LIABILITIES:
    Due to The Dreyfus Corporation and subsidiaries.........................                       $255,342
    Due to Distributor......................................................                         88,111
    Due to Custodian........................................................                         70,209
    Accrued expenses and other liabilities..................................                         211,146         624,808
                                                                                                      ______           _____
NET ASSETS..................................................................                                    $530,112,182
                                                                                                                     =======
REPRESENTED BY:
    Paid-in capital.........................................................                                    $530,126,596
    Accumulated net realized (loss) on investments..........................                                         (14,414)
                                                                                                                     _______
NET ASSETS at value.........................................................                                    $530,112,182
                                                                                                                     =======
Shares of Common Stock Outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                     530,068,468
                                                                                                                     =======
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                         58,128
                                                                                                                     =======
NET ASSET VALUE per share:
    Class A Shares
      ($530,054,054 / 530,068,468 shares)...................................                                         $1.00
                                                                                                                     =======
    Class B Shares
      ($58,128 / 58,128 shares).............................................                                         $1.00
                                                                                                                     =======







See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                  YEAR ENDED JANUARY 31, 1996
<S>                                                                                              <C>             <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                     $31,797,634
    EXPENSES:
      Management fee-Note 2(a)..............................................                     $2,622,700
      Distribution fees (Class A & B Shares)-Note 2(b)......................                       1,049,080
      Shareholder servicing costs-Note 2(c).................................                         371,882
      Custodian fees........................................................                         134,955
      Registration fees.....................................................                          95,108
      Professional fees.....................................................                          56,602
      Prospectus and shareholders' reports..................................                          36,368
      Directors' fees and expenses-Note 2(d)................................                          33,543
      Miscellaneous.........................................................                           5,157
                                                                                                       _____
          TOTAL EXPENSES....................................................                       4,405,395
      Less-reduction in shareholder servicing costs
          due to undertaking-Note 2(c)......................................                              43
                                                                                                       _____
          NET EXPENSES......................................................                                         4,405,352
                                                                                                                        ______
INVESTMENT INCOME-NET.......................................................                                        27,392,282
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                            (9,720)
                                                                                                                        ______
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                       $27,382,562
                                                                                                                       =======




See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                                     YEAR ENDED JANUARY 31,
                                                                                    ______________________________________
                                                                                           1995                        1996
                                                                                         ________                      ________
<S>                                                                             <C>                           <C>
OPERATIONS:
    Investment income-net................................................       $      20,068,028             $      27,392,282
    Net realized (loss) on investments...................................                  (4,571)                       (9,720)
                                                                                         ________                      ________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS...........              20,063,457                    27,382,562
                                                                                         ________                      ________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares.....................................................              (20,068,028)                  (27,390,125)
      Class B shares.....................................................                   __                            (2,157)
                                                                                         ________                      ________
          TOTAL DIVIDENDS................................................              (20,068,028)                  (27,392,282)
                                                                                         ________                      ________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares.....................................................             4,356,251,849               4,619,394,913
      Class B shares.....................................................                   __                           97,286
    Dividends reinvested:
      Class A shares.....................................................                19,433,620                  26,433,785
      Class B shares.....................................................                    __                           2,087
    Cost of shares redeemed:
      Class A shares.....................................................            (4,399,218,939)             (4,629,110,398)
      Class B shares.....................................................                    __                         (41,245)
                                                                                         ________                      ________
          INCREASE (DECREASE) IN NET ASSETS FROM
            CAPITAL STOCK TRANSACTIONS...................................              (23,533,470)                  16,776,428
                                                                                         ________                      ________
            TOTAL INCREASE (DECREASE) IN NET ASSETS......................              (23,538,041)                  16,766,708
NET ASSETS:
    Beginning of year....................................................              536,883,515                  513,345,474
                                                                                         ________                      ________
    End of year..........................................................          $    513,345,474                $530,112,182
                                                                                         ========                      ========




See notes to financial statements.
</TABLE>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS

Reference is made to page 4 of the Fund's Prospectus dated
June 3, 1996.


See notes to financial statements.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    General Government Securities Money Market Fund, Inc. (the "Fund") is
registered under the Investment Company Act of 1940 ("Act") as a diversified
open-end management investment company. The Fund's investment objective is to
provide investors with as high a level of current income as is consistent
with the preservation of capital and the maintenance of liquidity. The
Dreyfus Corporation ("Manager") serves as the Fund's investment adviser. The
Manager is a direct subsidiary of Mellon Bank, N.A.
    Premier Mutual Fund Services, Inc. (the "Distributor") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales load. 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
the 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.
    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.
    (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 (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, it is the policy of the Fund not to distribute such
gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, if such qualification is in the
best interests of its shareholders, by complying with the applicable
provisions of the Internal Revenue Code, and to make distributions of taxable
income sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $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 January 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 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 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, 1996, pursuant to the Agreement.
    Effective December 1, 1995, 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 $11,715 for the period from
December 1, 1995 through January 31, 1996.
    (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 implementing and of operating the Plan. In
addition, the Fund reimburses (a) the Distributor for payments made for
distributing Class A shares and servicing shareholder accounts ("Servicing")
and (b) the Manager, Dreyfus Service Corporation, a wholly-owned subsidiary
of the Manager, and their affiliates (collectively "Dreyfus") for payments
made for Servicing, at an aggregate annual rate of up to .20 of 1% of the
value of the Fund's average daily net assets of Class A. Both the Distributor
and Dreyfus may pay Service Agents (a 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
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
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 year ended January 31, 1996,
$1,048,994 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, 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 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. For the period March
31, 1995 through January 31, 1996, $86 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 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 year ended January 31, 1996,
the Fund was charged an aggregate of $229,788 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"), effective March 31, 1995, 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 (excluding 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. For the period
March 31, 1995 through January 31, 1996, $108 was charged to the Fund
pursuant to the Class B Shareholder Services Plan, of which $43 was
reimbursed by the Manager.
    (D) Each director who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $500
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
    We have audited the accompanying statement of assets and liabilities of
General Government Securities Money Market Fund, Inc., including the
statement of investments, as of January 31, 1996, 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, 1996 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, 1996, 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 and Young LLP signature logo]

New York, New York
March 6, 1996
 




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