SELIGMAN HENDERSON GLOBAL FUND SERIES INC
497, 2000-10-05
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                    Supplement, dated October 5, 2000, to the
                        Prospectus, dated March 1, 2000,
               of Seligman Global Fund Series, Inc. (the "Series")
                                on behalf of its
               Seligman Global Growth Fund ("Global Growth Fund")
    Seligman Global Smaller Companies Fund ("Global Smaller Companies Fund")
        Seligman International Growth Fund ("International Growth Fund")


Global Smaller Companies Fund:

     The definition of "smaller  companies"  appearing in the highlighted box on
page 10 of the Series' Prospectus has been revised as follows:

               "Smaller  Companies:  Companies  with  market
                capitalization,  at the  time  of purchase by
                the Fund, equivalent to US $2 billion or less."


Global Growth Fund and International Growth Fund:

     The following  information replaces the paragraphs under "Management of the
Funds - Portfolio  Management" under the section "International Growth Fund and
Global Growth Fund" on pages 22 and 23 of the Series' Prospectus:

"The  International  Growth  Fund and the  Global  Growth  Fund are  managed  by
Seligman's Global Growth Team, which is headed by Ms. Marion S. Schultheis.

Ms. Schultheis joined Seligman in May 1998 as a Managing Director. She is a Vice
President of Seligman Global Fund Series, Inc. and has been Portfolio Manager of
the Global Growth Fund since joining Seligman.  Prior to joining  Seligman,  Ms.
Schultheis  was a Managing  Director at Chancellor  LGT from October 1997 to May
1998 and Senior Portfolio Manager at IDS Advisory Group Inc. from August 1987 to
October 1997.  Ms.  Schultheis  also manages  Seligman  Capital  Fund,  Inc. and
Seligman Growth Fund, Inc. She is a Vice President of Seligman Portfolios,  Inc.
and Portfolio  Manager of its Seligman  Capital  Portfolio,  Seligman  Large-Cap
Growth Portfolio. The Global Growth Team, which she heads, also manages Seligman
Global Growth Portfolio and Seligman International Growth Portfolio."




EQSGF1S2-10/2000



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