GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
485BPOS, 1996-02-20
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                                          Securities Act File No. 2-77207
                                  Investment Company Act File No. 811-3456
==========================================================================
                     SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C. 20549
                                  FORM N-1A
                                                                         
REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933               /x/
                                                                            
           Pre-Effective Amendment No. __                             / / 
                                                                           
           Post-Effective Amendment No. 20                            /x/

                     and
                                                                          
REGISTRATION STATEMENT UNDER THE INVESTMENT COMPANY ACT OF 1940       /x/
                                                                         
           Amendment No. 20                                           /x/ 

              (Check appropriate box or boxes)

            GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
             (Exact Name of Registrant as Specified in Charter)

c/o The Dreyfus Corporation
200 Park Avenue, New York, New York                   10166
(Address of Principal Executive Offices)           (Zip Code)

Registrant's Telephone Number, including Area Code:  (212) 922-6000

                            Mark N. Jacobs, Esq.
                               200 Park Avenue
                          New York, New York  10166
                   (Name and Address of Agent for Service)
                                      
                                  copy to:
                                      
                             Lewis G. Cole, Esq.
                          Stroock & Stroock & Lavan
                              7 Hanover Square
                       New York, New York  10004-2696

           It is proposed that this filing will become effective (check
appropriate box) 

             x  immediately upon filing pursuant to paragraph (b)

                on (date) pursuant to paragraph (b)

           ____ 60 days after filing pursuant to paragraph (a)(i)

                on (date) pursuant to paragraph (a)(i)

                75 days after filing pursuant to paragraph (a)(ii)

                on (date) pursuant to paragraph (a)(ii) of Rule 485.

           If appropriate, check the following box:

  this post-effective amendment designates a new effective date
   for a previously filed post-effective amendment.

Registrant has registered an indefinite number of its shares of its common
stock under the Securities Act of 1933 pursuant to Section 24(f) of the
Investment Company Act of 1940.  Registrant's Rule 24f-2 Notice for its
fiscal year ended January 31, 1996 is expected to be filed on or about
March 29, 1996.


         GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.

                       PART C. OTHER INFORMATION


Item 24. Financial Statements and Exhibits

(a)       Financial Statements:

          Included in Part A of the Registration Statement 
          filed March 31, 1995:
            Condensed Financial Information for the 
             ten years ended January 31, 1995.

          Included in Part B of the Registration Statement filed
          March 31, 1995:
          
            Statement of Investments -- January 31, 1995.
            Statement of Assets and Liabilities -- January 31, 1995.
            Statement of Operations -- for the year ended
             January 31, 1995.
            Statement of Changes in Net Assets -- for each of the
             two years ended January 31, 1995.
            Notes to Financial Statements.
            Report of Ernst & Young LLP, Independent Auditors,
             dated March 6, 1995.

All schedules and other financial statement information, for which
provision is made in the applicable accounting regulations of the
Securities and Exchange Commission, are either omitted because they are
not required under the related instructions, they are inapplicable, or
the required information is presented in the financial statements or
notes thereto which are included in Part B of the Registration
Statement.


(b)       Exhibits:

          (1)     Articles of Incorporation and Articles of Amendment
                  are incorporated by reference to Exhibits (1) (a) and
                  (1)(b), respectively, of Post-Effective Amendment
                  No. 18 to the Registration Statement on Form N-1A,
                  filed March 31, 1995.

          (2)     By-Laws, as amended, are incorporated by reference to
                  Exhibit (2) of Post-Effective Amendment No. 18 to the
                  Registration Statement on Form N-1A, filed March 31,
                  1995.

          (5)     Management Agreement is incorporated by reference to
                  Exhibit (5) of Post-Effective Amendment No. 18 to the
                  Registration Statement on Form N-1A, filed March 31,
                  1995.

          (6)(a)  Distribution Agreement is incorporated by reference
                  to Exhibit (6)(a) of Post-Effective Amendment No. 18
                  to the Registration Statement on Form N-1A, filed
                  March 31, 1995.

          (6)(b)  Form of Service Agreement is incorporated by
                  reference to Exhibit (6)(b) of Post-Effective
                  Amendment No. 18 to the Registration Statement on
                  Form N-1A, filed March 31, 1995.

          (8)     Amended and Restated Custody Agreement is
                  incorporated by reference to Exhibit (8)(a) of Post-
                  Effective Amendment No. 18 to the Registration
                  Statement on Form N-1A, filed on March 31, 1995.

          (9)(a)  Shareholder Services Plan (Class A) is incorporated
                  by reference to Exhibit (9)(a) of Post-Effective
                  Amendment No. 17 to the Registration Statement on
                  Form N-1A, filed on January 30, 1995.

          (9)(b)  Shareholder Services Plan (Class B) is incorporated
                  by reference to Exhibit (9)(b) of Post-Effective
                  Amendment No. 17 to the Registration Statement on
                  Form N-1A, filed on January 30, 1995.
        
          (10)    Opinion, including consent, of Stroock & Stroock &
                  Lavan is incorporated by reference to Exhibit (10) of
                  Post-Effective Amendment No. 18 to the Registration
                  Statement on Form N-1A, filed March 31, 1995.

          (15)(a) Service Plan (Class A) is incorporated by reference
                  to Exhibit (15)(a) of Post-Effective Amendment No. 17
                  to the Registration Statement on Form N-1A, filed
                  January 30, 1995.

          (15)(b) Distribution Plan (Class B) is incorporated by
                  reference to Exhibit (15)(b) of Post-Effective
                  Amendment No. 17 to the Registration Statement on
                  Form N-1A, filed on January 30, 1995.

          (16)    Schedules of Computation of Performance Data are
                  incorporated by reference to Exhibit (16) of Post-
                  Effective Amendment No. 16 to the Registration
                  Statement on Form N-1A, filed on May 18, 1994.

          (18)    Rule 18f-3 Plan.


          Other Exhibits:

          (a)     Powers of Attorney are incorporated by reference to
                  Other Exhibits of Post-Effective Amendment No. 17 to
                  the Registration Statement on Form N-1A, filed on
                  January 30, 1995.

          (b)     Assistant Secretary's Certificate is incorporated by
                  reference to Other Exhibits of Post-Effective
                  Amendment No. 17 to the Registration Statement on
                  Form N-1A, filed on January 30, 1995.

Item 25.  Persons Controlled by or Under Common Control with Registrant

          Not applicable.


Item 26.  Number of Holders of Securities

                                                  (2)
                                                  Number of Record
        (1)                                       Holders as of
        Title of Class                            February 16, 1996

        Common Stock, par value
        $.01 per share      

        Class A                                       3,829

        Class B                                       8


Item 27.  Indemnification

        The Statement as to the general effect of any contract,
arrangements or statute under which a director, officer, underwriter or
affiliated person of the Registrant is insured or indemnified in any
manner against any liability which may be incurred in such capacity,
other than insurance provided by any director, officer, underwriter or
affiliated person for its own protection, is incorporated by reference
to Item 27 of Part C of Post-Effective Amendment No. 18 to the
Registration Statement on Form N-1A, filed on March 31, 1995.

        Reference also is made to the Distribution Agreement filed as
Exhibit 6(a) to Post-Effective Amendment No. 18 to the Registration
Statement on Form N-1A.

Item 28.  Business and Other Connections of Investment Adviser

        The Dreyfus Corporation ("Dreyfus") and subsidiary companies
comprise a financial service organization whose business consists
primarily of providing investment management services as the investment
adviser, manager and distributor for sponsored investment companies
registered under the Investment Company Act of 1940 and as an
investment adviser to institutional and individual accounts.  Dreyfus
also serves as sub-investment adviser to and/or administrator of other
investment companies.  Dreyfus Service Corporation, a wholly-owned
subsidiary of Dreyfus, is a registered broker-dealer.  Dreyfus
Management, Inc., another wholly-owned subsidiary, provides investment
management services to various pension plans, institutions and
individuals.

Officers and Directors of Dreyfus

Name and Position with
Dreyfus                                  Other Businesses

MANDELL L. BERMAN             Real estate consultant and private
Director                      investor
                                29100 Northwestern Highway--Suite 370
                                Southfield, Michigan 48034;
                              Past Chairman of the Board of Trustees of
                              Skillman Foundation;
                              Member of the Board of Vintners
                                International

FRANK V. CAHOUET              Chairman of the Board, President and
Director                      Chief Executive Officer:
                                Mellon Bank Corporation****;
                                Mellon Bank, N.A.****;
                              Director:
                                Avery Dennison Corporation
                                150 North Orange Grove Boulevard
                                Pasadena, California 91103;
                                Saint-Gobain Corporation
                                750 East Swedesford Road
                                Valley Forge, Pennsylvania 19482;
                                Teledyne, Inc.
                                1901 Avenue of the Stars
                                Los Angeles, California 90067

ALVIN E. FRIEDMAN             Senior Adviser to Dillon, Read & Co. Inc.
Director                        535 Madison Avenue
                                New York, New York 10022;
                              Director and member of the Executive
                              Committee of Avnet, Inc.**

HOWARD STEIN                  Chairman of the Board:
Chairman of the Board           Dreyfus Acquisition Corporation*;
and Chief Executive             The Dreyfus Consumer Credit
Officer                         Corporation*;
                              Dreyfus Management, Inc.*;
                                Dreyfus Service Corporation*;
                              Chairman of the Board and Chief Executive
                              Officer:
                                Major Trading Corporation*;
                              Director:
                                Avnet, Inc.**;
                                Dreyfus America Fund++++;
                                The Dreyfus Fund International
                                Limited+++++;
                                Dreyfus Partnership Management, Inc.*;
                                Dreyfus Personal Management, Inc.*;
                                Dreyfus Precious Metals, Inc.*;
                                Dreyfus Service Organization, Inc.***;
                                Seven Six Seven Agency, Inc.*;
                                World Balanced Fund+++;
                              Trustee:
                                Corporate Property Investors
                                New York, New York

W. KEITH SMITH                Chairman and Chief Executive Officer:
Vice Chairman of the Board      The Boston Company*****;
                              Vice Chairman of the Board:
                                Mellon Bank Corporation****;
                                Mellon Bank, N.A.****;
                              Director:
                                Dentsply International, Inc.
                                570 West College Avenue
                                York, Pennsylvania 17405

CHRISTOPHER M. CONDRON        Vice Chairman:
President, Chief                Mellon Bank Corporation****;
Operating Officer and           The Boston Company*****;
Director                 Deputy Director:
                                Mellon Trust****;
                              Chief Executive Officer:
                                The Boston Company Asset Management,
                                Inc.*****;
                              President:
                                Boston Safe Deposit and Trust
                                Company*****

STEPHEN E. CANTER             Former Chairman and Chief Executive
Vice Chairman, Chief          Officer:
Investment Officer and          Kleinwort Benson Investment Management
a Director                      Americas Inc.*

LAWRENCE S. KASH              Chairman, President and Chief
Vice Chairman--Distribution   Executive Officer:
and a Director                  The Boston Company Advisors, Inc.
                                53 State Street
                                Exchange Place
                                Boston, Massachusetts 02109;
                              Executive Vice President and Director: 
                                Dreyfus Service Organization, Inc.***;
                              Director: 
                                The Dreyfus Consumer Credit
                                Corporation*; 
                                The Dreyfus Trust Company++; 
                                Dreyfus Service Corporation*;
                              President:
                                The Boston Company*****;
                                Laurel Capital Advisors****;
                                Boston Group Holdings, Inc.;
                              Executive Vice President:
                                Mellon Bank, N.A.****;
                                Boston Safe Deposit & Trust*****;

LAWRENCE M. GREENE            Director:
Director                        Dreyfus America Fund++++

JULIAN M. SMERLING            None
Director

PHILIP L. TOIA                Chairman of the Board and Trust
Vice Chairman--               Investment Officer:
Operations and                  The Dreyfus Trust Company++;
Administration                Chairman of the Board and Chief
and a Director                Executive Officer:
                                Major Trading Corporation*;
                              Director:
                                The Dreyfus Security Savings Bank,
                                F.S.B.+;
                                Dreyfus Service Corporation*;
                                Seven Six Seven Agency, Inc.*;
                              President and Director:
                                Dreyfus Acquisition Corporation*;
                                The Dreyfus Consumer Credit
                                Corporation*;
                                Dreyfus-Lincoln, Inc.*;
                                Dreyfus Management, Inc.*;
                                Dreyfus Personal Management, Inc.*;
                                Dreyfus Partnership Management, Inc.+;
                                Dreyfus Service Organization***;
                                The Truepenny Corporation*;
                              Formerly, Senior Vice President:
                                The Chase Manhattan Bank, N.A. and
                                The Chase Manhattan Capital Markets
                                Corporation
                                One Chase Manhattan Plaza
                                New York, New York 10081

WILLIAM T. SANDALLS, JR.      None
Senior Vice President and
Chief Financial Officer

BARBARA E. CASEY              President:
Vice President--                Dreyfus Retirement Services Division;
Dreyfus Retirement            Executive Vice President:
Services                        Boston Safe Deposit & Trust Co.*****;
                                Dreyfus Service Corporation*

DIANE M. COFFEY               None
Vice President--
Corporate Communications

ELIE M. GENADRY               President:
Vice President--                Institutional Services Division of
Institutional Sales             Dreyfus Service Corporation*;
                                Broker-Dealer Division of Dreyfus      
                                Service Corporation*;
                                Group Retirement Plans Division of
                                Dreyfus Service Corporation*;
                              Executive Vice President:
                                Dreyfus Service Corporation*;
                                Dreyfus Service Organization, Inc.***;
                              Vice President:
                                The Dreyfus Trust Company++

DANIEL C. MACLEAN             Director, Vice President and Secretary:
Vice President and              Dreyfus Precious Metals, Inc.*;
General Counsel               Director and Vice President:
                                The Dreyfus Consumer Credit
                                Corporation*;
                              Director and Secretary:
                                Dreyfus Partnership Management, Inc.*;
                                Major Trading Corporation*;
                                The Truepenny Corporation+;
                              Director:
                                The Dreyfus Trust Company++;
                              Secretary:
                                Dreyfus Service Corporation*;
                                Dreyfus Service Organization, Inc.***;
                                Seven Six Seven Agency, Inc.*

JEFFREY N. NACHMAN            None
Vice President--Mutual
Fund Accounting

WILLIAM F. GLAVIN, JR.        Senior Vice President:
Vice President--Corporate       The Boston Company Advisors, Inc.
Development                     53 State Street
                                Exchange Place
                                Boston, Massachusetts 02109

ANDREW S. WASSER              Vice President:
Vice President--Information     Mellon Bank Corporation****
Services                        

MAURICE BENDRIHEM             Treasurer:
Controller                      Dreyfus Partnership Management,
                                  Inc.***;
                                Dreyfus Service Organization, Inc.***;
                                Seven Six Seven Agency, Inc.*;
                                The Truepenny Corporation*;
                              Controller:
                                Dreyfus Acquisition Corporation*;
                                The Dreyfus Trust Company++;
                                The Dreyfus Consumer Credit
                                Corporation*;
                              Assistant Treasurer:
                                Dreyfus Precious Metals*;
                              Formerly, Vice President-Financial
                              Planning, Administration and Tax:
                                Showtime/The Movie Channel, Inc.
                                1633 Broadway
                                New York, New York 10019

MARK N. JACOBS                Vice President, Secretary and Director: 
Vice President--                Lion Management, Inc.*;                
Legal and Secretary           Secretary:
                                The Dreyfus Consumer Credit
                                Corporation*;
                                Dreyfus Management, Inc.*;
                              Assistant Secretary:
                                Dreyfus Service Organization, Inc.***;
                                Major Trading Corporation*;
                                The Truepenny Corporation*

ELVIRA OSLAPAS                Assistant Secretary:
Assistant Secretary             Dreyfus Service Corporation*;
                                Dreyfus Management, Inc.*;
                                Dreyfus Acquisition Corporation, Inc.*;
                                The Truepenny Corporation*
                  

*         The address of the business so indicated is 200 Park Avenue,
          New York, New York 10166.
**        The address of the business so indicated is 80 Cutter Mill
          Road, Great Neck, New York 11021.
***       The address of the business so indicated is 131 Second
          Street, Lewes, Delaware 19958.
****      The address of the business so indicated is One Mellon Bank
          Center, Pittsburgh, Pennsylvania 15258.
*****     The address of the business so indicated is One Boston Place,
          Boston, Massachusetts 02108.
+         The address of the business so indicated is Atrium Building,
          80 Route 4 East, Paramus, New Jersey 07652.
++        The address of the business so indicated is 144 Glenn Curtiss
          Boulevard, Uniondale, New York 11556-0144.
+++       The address of the business so indicated is One Rockefeller
          Plaza, New York, New York 10020.
++++      The address of the business so indicated is 2 Boulevard
          Royal, Luxembourg.
+++++     The address of the business so indicated is Nassau, Bahamas
          Islands.

Item 29.  Principal Underwriters

          (a)  Other investment companies for which Registrant's prin-
               cipal underwriter (exclusive distributor) acts as
               principal underwriter or exclusive distributor:

           1.  Comstock Partners Strategy Fund, Inc.
           2.  Dreyfus A Bonds Plus, Inc.
           3.  Dreyfus Appreciation Fund, Inc.
           4.  Dreyfus Asset Allocation Fund, Inc.
           5.  Dreyfus Balanced Fund, Inc.
           6.  Dreyfus BASIC GNMA Fund
           7.  Dreyfus BASIC Money Market Fund, Inc.
           8.  Dreyfus BASIC Municipal Fund, Inc.
           9.  Dreyfus BASIC U.S. Government Money Market Fund
          10.  Dreyfus California Intermediate Municipal Bond Fund
          11.  Dreyfus California Tax Exempt Bond Fund, Inc.
          12.  Dreyfus California Tax Exempt Money Market Fund
          13.  Dreyfus Capital Value Fund (A Premier Fund)
          14.  Dreyfus Cash Management
          15.  Dreyfus Cash Management Plus, Inc.
          16.  Dreyfus Connecticut Intermediate Municipal Bond Fund
          17.  Dreyfus Connecticut Municipal Money Market Fund, Inc.
          18.  Dreyfus Edison Electric Index Fund, Inc.
          19.  Dreyfus Florida Intermediate Municipal Bond Fund
          20.  Dreyfus Florida Municipal Money Market Fund
          21.  The Dreyfus Fund Incorporated
          22.  Dreyfus Global Bond Fund, Inc.
          23.  Dreyfus Global Growth, L.P. (A Strategic Fund)
          24.  Dreyfus GNMA Fund, Inc.
          25.  Dreyfus Government Cash Management
          26.  Dreyfus Growth and Income Fund, Inc.
          27.  Dreyfus Growth and Value Fund, Inc.
          28.  Dreyfus Growth Opportunity Fund, Inc.
          29.  Dreyfus Institutional Money Market Fund
          30.  Dreyfus Institutional Short Term Treasury Fund
          31.  Dreyfus Insured Municipal Bond Fund, Inc.
          32.  Dreyfus Intermediate Municipal Bond Fund, Inc.
          33.  Dreyfus International Equity Fund, Inc.
          34.  Dreyfus International Recovery Fund, Inc.
          35.  The Dreyfus/Laurel Funds, Inc.
          36.  The Dreyfus/Laurel Funds Trust
          37.  The Dreyfus/Laurel Tax-Free Municipal Funds
          38.  The Dreyfus/Laurel Investment Series
          39.  Dreyfus Life and Annuity Index Fund, Inc.
          40.  Dreyfus LifeTime Portfolios, Inc.
          41.  Dreyfus Liquid Assets, Inc.
          42.  Dreyfus Massachusetts Intermediate Municipal Bond Fund
          43.  Dreyfus Massachusetts Municipal Money Market Fund
          44.  Dreyfus Massachusetts Tax Exempt Bond Fund
          45.  Dreyfus Michigan Municipal Money Market Fund, Inc.
          46.  Dreyfus Money Market Instruments, Inc.
          47.  Dreyfus Municipal Bond Fund, Inc.
          48.  Dreyfus Municipal Cash Management Plus
          49.  Dreyfus Municipal Money Market Fund, Inc.
          50.  Dreyfus New Jersey Intermediate Municipal Bond Fund
          51.  Dreyfus New Jersey Municipal Bond Fund, Inc.
          52.  Dreyfus New Jersey Municipal Money Market Fund, Inc.
          53.  Dreyfus New Leaders Fund, Inc.
          54.  Dreyfus New York Insured Tax Exempt Bond Fund
          55.  Dreyfus New York Municipal Cash Management
          56.  Dreyfus New York Tax Exempt Bond Fund, Inc.
          57.  Dreyfus New York Tax Exempt Intermediate Bond Fund
          58.  Dreyfus New York Tax Exempt Money Market Fund
          59.  Dreyfus Ohio Municipal Money Market Fund, Inc.
          60.  Dreyfus 100% U.S. Treasury Intermediate Term Fund
          61.  Dreyfus 100% U.S. Treasury Long Term Fund
          62.  Dreyfus 100% U.S. Treasury Money Market Fund
          63.  Dreyfus 100% U.S. Treasury Short Term Fund
          64.  Dreyfus Pennsylvania Intermediate Municipal
                 Bond Fund
          65.  Dreyfus Pennsylvania Municipal Money Market Fund
          66.  Dreyfus Short-Intermediate Government Fund
          67.  Dreyfus Short-Intermediate Municipal Bond Fund
          68.  Dreyfus Short-Term Income Fund, Inc.
          69.  The Dreyfus Socially Responsible Growth Fund, Inc.
          70.  Dreyfus Strategic Growth, L.P.
          71.  Dreyfus Strategic Income
          72.  Dreyfus Strategic Investing
          73.  Dreyfus Tax Exempt Cash Management
          74.  The Dreyfus Third Century Fund, Inc.
          75.  Dreyfus Treasury Cash Management
          76.  Dreyfus Treasury Prime Cash Management
          77.  Dreyfus Variable Investment Fund
          78.  Dreyfus-Wilshire Target Funds, Inc.
          79.  Dreyfus Worldwide Dollar Money Market Fund, Inc.
          80.  General California Municipal Bond Fund, Inc.
          81.  General California Municipal Money Market Fund
          82.  General Government Securities Money Market
                 Fund, Inc.
          83.  General Money Market Fund, Inc.
          84.  General Municipal Bond Fund, Inc.
          85.  General Municipal Money Market Fund, Inc.
          86.  General New York Municipal Bond Fund, Inc.
          87.  General New York Municipal Money Market Fund
          88.  Pacifica Funds Trust--Pacific American Money Market
               Portfolio, Pacific American U.S. Treasury Portfolio
          89.  Peoples Index Fund, Inc.
          90.  Peoples S&P MidCap Index Fund, Inc.
          91.  Premier California Municipal Bond Fund
          92.  Premier Equity Funds, Inc.
          93.  Premier Global Investing, Inc.
          94.  Premier GNMA Fund
          95.  Premier Growth Fund, Inc.
          96.  Premier Insured Municipal Bond Fund
          97.  Premier Municipal Bond Fund
          98.  Premier New York Municipal Bond Fund
          99.  Premier State Municipal Bond Fund


          (b)

Name and principal
business address       Positions and offices with  Positions and 
                        Premier Mutual             offices with
                       Fund Services, Inc.         Registrant

Marie E. Connolly+ Director, President, Chief      President and
                   Executive Officer and           Treasurer
                   Compliance Officer             

Joseph F. Tower, III+  Senior Vice President,       Assistant
                       Treasurer and Chief          Treasurer
                       Financial Officer      

John E. Pelletier+    Senior Vice President,        Vice President
                      General Counsel, Secretary    and Secretary
                        and Clerk                  

Frederick C. Dey++    Senior Vice President         Vice President
                                                    and Assistant
                                                    Treasurer

Eric B. Fischman++      Vice President and        Vice President
                      Associate General Counsel   and Assistant
                                                  Secretary

Paul Prescott+        Vice President              None

Elizabeth Bachman+    Assistant Vice President  Vice President
                                                and Assistant
                                                Secretary

Mary Nelson+         Assistant Treasurer       None

John J. Pyburn++      Assistant Treasurer     Assistant
                                              Treasurer

Jean M. O'Leary+      Assistant Secretary and    None
                      Assistant Clerk

John W. Gomez+        Director                   None

William J. Nutt+      Director                   None

                            
+    Principal business address is One Exchange Place, Boston, Massa-
     chusetts 02109.
++   Principal business address is 200 Park Avenue, New York, New York
     10166.

Item 30.  Location of Accounts and Records

          1.   First Data Investors Services Group, Inc.,
               a subsidiary of First Data Corporation
               P.O. Box 9671
               Providence, Rhode Island 02940-9671

          2.   The Bank of New York
               90 Washington Street
               New York, New York 10286

          3.   Dreyfus Transfer, Inc.
               P.O. Box 9671
               Providence, Rhode Island  02940-9671

          4.   The Dreyfus Corporation
               200 Park Avenue
               New York, New York 10166

Item 31.  Management Services

          Not Applicable.

Item 32.  Undertakings

          Registrant hereby undertakes to call a meeting of
shareholders for the purpose of voting upon the question of removal of
a director or directors when requested in writing to do so by the
holders of at least 10% of the Registrant's outstanding shares of
common stock and in connection with such meeting to comply with the
provisions of Section 16(c) of the Investment Company Act of 1940
relating to shareholder communications.
<PAGE>
                              SIGNATURES

          Pursuant to the requirements of the Securities Act of 1933
and the Investment Company Act of 1940, the Registrant certifies that
it meets all of the requirements for effectiveness of this Amendment to
the Registration Statement pursuant to Rule 485(b) under the Securities
Act of 1933 and has duly caused this Amendment to the Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of New York, and State of New York, on the 20th
day of February, 1996.

                            GENERAL GOVERNMENT SECURITIES MONEY MARKET
                              FUND, INC.
                            (Registrant)

                            By:/s/Marie E. Connolly*                 
                               Marie E. Connolly, President


        Pursuant to the requirements of the Securities Act of 1933,
this Amendment to the Registration Statement has been signed below by
the following persons in the capacities and on the dates indicated.

/s/Marie E. Connolly*            President and Treasurer  February 20, 1996
Marie E. Connolly                (Principal Executive 
                                 and Financial Officer)

/s/Joseph F. Tower, III*         Assistant Treasurer      February 20, 1996
Joseph F. Tower, III             (Principal Accounting 
                                 Officer)

/s/Clifford L. Alexander, Jr.*   Director                 February 20, 1996
Clifford L. Alexander, Jr.* 

/s/Peggy C. Davis*               Director                 February 20, 1996
Peggy C. Davis

/s/Joseph S. DiMartino           Director                 February 20, 1996
Joseph S. DiMartino

/s/Ernest Kakfa*                 Director                 February 20, 1996
Ernest Kakfa*

/s/Saul B. Klaman*               Director                 February 20, 1996
Saul B. Klaman

/s/Nathan Leventhal*             Director                 February 20, 1996
Nathan Leventhal

/s/Eric B. Fischman                                               
* By:  Eric B. Fischman,
       Attorney-in-Fact


       GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.

                Post-Effective Amendment No. 20 to
             Registration Statement on Form N-1A under
                  the Securities Act of 1933 and
                the Investment Company Act of 1940
                                       
                             EXHIBITS
                                         
                         INDEX TO EXHIBITS

                                             Page


(18)   Rule 18f-3 Plan. . . . . . . . . . . . . . . 

<PAGE>
                   THE DREYFUS FAMILY OF FUNDS
                    (General Family of Funds)

                         Rule 18f-3 Plan

          Rule 18f-3 under the Investment Company Act of 1940,
as amended (the "1940 Act"), requires that the Board of an
investment company desiring to offer multiple classes pursuant
to said Rule adopt a plan setting forth the separate arrangement
and expense allocation of each class, and any related conversion
features or exchange privileges.
          The Board, including a majority of the non-interested
Board members, of each of the investment companies, or series
thereof, listed on Schedule A attached hereto (each, a "Fund")
which desires to offer multiple classes has determined that the
following plan is in the best interests of each class
individually and the Fund as a whole:
          1. Class Designation:  Fund shares shall be divided
into Class A and Class B.

          2. Differences in Services:  The services offered to
shareholders of each Class shall be substantially the same,
except for certain services provided to each Class pursuant to
separate plans adopted by the Fund's Board.

          3. Differences in Distribution Arrangements:  Shares
of each Class shall be offered at net asset value.  Neither
class shall be subject to any front-end or contingent deferred
sales charges.
          
     Class A shares of each Fund listed on Schedule B
attached hereto shall be subject to annual payments for
distributing Class A shares and servicing shareholder accounts
at the rate of up to .20% of the value of the average daily net
assets of Class A pursuant to a Service Plan adopted in
accordance with Rule 12b-1 under the 1940 Act.
     
     Class B shares of each Fund shall be subject to annual
payments for distributing Class B shares at the rate of up to
 .20% of the value of the average daily net assets of Class B
pursuant to a Distribution Plan adopted in accordance with
Rule 12b-1 under the 1940 Act.  Class B shares shall be charged
directly for sub-accounting services at the annual rate of .05%
of the value of the average daily net assets of Class B.

          Each Class of shares shall be subject to a separate
Shareholder Services Plan.  Under the respective Shareholder
Services Plan, Class A shares shall be subject to payments in an
amount not to exceed an annual rate of .25% of the value of the
average daily net assets of Class A and Class B shares shall be
subject to an annual service fee at the rate of .25% of the
value of the average daily net assets of Class B.

          4. Expense Allocation.   The following expenses
shall be allocated, to the extent practicable, on a Class-by-
Class basis:  (a) fees under the Service Plan, if any,
Distribution Plan and Shareholder Services Plans; (b) printing
and postage expenses related to preparing and distributing
materials, such as shareholder reports, prospectuses and
proxies, to current shareholders of a specific Class;
(c) Securities and Exchange Commission and Blue Sky registration
fees incurred by a specific Class; (d) the expense of
administrative personnel and services as required to support the
shareholders of a specific Class; (e) litigation or other legal
expenses relating solely to a specific Class; (f) transfer agent
fees identified by the Fund's transfer agent as being
attributable to a specific Class; and (g) Board members' fees
incurred as a result of issues relating to a specific Class.

          5. Exchange Privileges.  Shares of a Class shall be
exchangeable only for shares of certain other investment
companies specified from time to time.

Dated:  July 19, 1995

                           SCHEDULE A


          General California Municipal Money Market Fund
          General Government Securities Money Market Fund, Inc.
          General Money Market Fund, Inc.
          General Municipal Money Market Fund, Inc.
          General New York Municipal Money Market Fund

                           SCHEDULE B


          General Government Securities Money Market Fund, Inc.
          General Money Market Fund, Inc.


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