GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
497, 1996-11-26
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                                                             November 25, 1996
             GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
                           Supplement to Prospectus
                              Dated June 3, 1996
        THE FOLLOWING INFORMATION SUPPLEMENTS AND SUPERSEDES ANY CONTRARY
INFORMATION CONTAINED IN THE SECTION OF THE FUND'S PROSPECTUS ENTITLED "HOW
TO BUY SHARES":
        Fund shares are sold on a continuous basis at the net asset value per
share next determined after an order in proper form and Federal Funds (monies
of member banks within the Federal Reserve System which are held on deposit
at a Federal Reserve Bank) are received by the Transfer Agent or other agent
or entity subject to the direction of such agents in written or telegraphic
form, or by Wells Fargo Bank, N.A. in telegraphic form.
        The Fund's net asset value per share is determined twice each day the
New York Stock Exchange or the Transfer Agent is open for business:  as of
5:00 p.m., New York time/2:00 p.m., California time, and as of 8:00 p.m., New
York time/5:00 p.m., California time.
        Qualified institutions may telephone orders for purchase of Fund
shares. A telephone order will become effective at the price determined at
5:00 p.m., New York time/2:00 p.m., California time, on a given day, and the
shares purchased will receive the dividend on Fund shares declared on that
day, if such order is placed to the Distributor or its designee in New York
by 5:00 p.m., New York time, or in California by 12:00 Noon, California time,
and Federal Funds are received by 6:00 p.m., New York time/3:00 p.m.,
California time, on that day.  A telephone order placed to the Distributor or
its designee in New York after 5:00 p.m., New York time, or in California
after 12:00 Noon, California time, but by 8:00 p.m., New York time/5:00 p.m.,
California time, on a given day will become effective at the price determined
at 8:00 p.m., New York time/5:00 p.m., California time, on that day if
Federal Funds are received by 11:00 a.m., New York time, on the next business
day.  The shares so purchased will begin to accrue dividends on the business
day following the date the order became effective.

                         (CONTINUED ON REVERSE SIDE)

        THE FOLLOWING INFORMATION SUPPLEMENTS AND SUPERSEDES ANY CONTRARY
INFORMATION CONTAINED IN THE SECTION OF THE FUND'S PROSPECTUS ENTITLED "HOW
TO REDEEM SHARES -- PROCEDURES -- REDEMPTION THROUGH A SELECTED DEALER":
        If the Selected Dealer transmits the redemption request so that it is
received by 5:00 p.m., New York time/2:00 p.m., California time, on a
business day, the proceeds of the redemption ordinarily will be transmitted
in Federal Funds on the same day and the shares will not receive the dividend
declared on that day.  If the redemption request is received after such time,
but by 8:00 p.m., New York time/5:00 p.m., California time, the redemption
request will be effective on that day, the shares will receive the dividend
declared on that day and the proceeds of redemption ordinarily will be
transmitted in Federal Funds on the next business day.
                                                                    975s112596


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