SELIGMAN HENDERSON GLOBAL FUND SERIES INC
497, 2000-01-21
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    Supplement, dated January 21, 2000, to the Prospectus, dated June 1, 1999
                                       of
              Seligman Global Fund Series, Inc. (the "Corporation")
             (formerly, Seligman Henderson Global Fund Series, Inc.)


The following  supersedes the related information set forth in the Corporation's
prospectus.

On January 21, 2000,  pursuant to authorization from the Corporation's  Board of
Directors,  J. & W.  Seligman & Co.  Incorporated,  manager  of the  Corporation
("Seligman"), gave notice to Henderson Investment Management Limited ("HIML") of
its termination, effective as of the close of business on March 31, 2000, of the
Subadvisory  Agreement  between  Seligman  and HIML in respect  of the  Seligman
Henderson  International  Fund, the Seligman  Henderson  Emerging Markets Growth
Fund, the Seligman Henderson Global Growth  Opportunities Fund, and the Seligman
Henderson Global Technology Fund (the "Funds"). At this time, HIML will continue
to act as  subadvisor  with respect to the  Seligman  Henderson  Global  Smaller
Companies Fund.

International  advisory  services  will be provided  to the Funds by  Seligman's
Global  Growth  Team,  Emerging  Markets  Team or  Global  Technology  Team,  as
described  below.  During the notice  period,  HIML will continue to provide the
Funds with  investment  advice,  research and  assistance  with respect to their
non-US  investments,  subject to Seligman's overall  supervision.  Following the
close of business on March 31, 2000,  Seligman  will assume full  responsibility
for the non-US investments of the Funds.

Seligman's  Global  Growth  Team  will  be  responsible  for  the  international
investments of the International Fund and the Global Growth  Opportunities Fund.
The Global Growth Team is co-headed by Ms. Marion S.  Schultheis and Mr. Jack P.
Chang.

Ms. Schultheis joined Seligman in May 1998 as a Managing Director. She is a Vice
President of the  Corporation  and has been  Co-Portfolio  Manager of the Global
Growth  Opportunities  Fund  since  May 1998.  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 and Seligman  Large-Cap
Growth Portfolio and Co-Portfolio  Manager of its Seligman  International Growth
Portfolio and Seligman Global Growth Portfolio.

Mr. Chang joined Seligman on September 20, 1999 as a Managing Director.  He is a
Vice President of the Corporation.  Prior to joining  Seligman,  Mr. Chang was a
Senior Vice  President and  Portfolio  Manager at Putnam  Investment  Management
since 1997. Prior thereto,  he was a Portfolio Manager with Columbia  Management
Company  from 1993 to 1997,  and a Senior  Analyst and  Portfolio  Manager  with
Scudder,  Stevens & Clark from 1989 to 1993.  Mr. Chang is also a Vice President
of  Seligman   Portfolios,   Inc.  and  Co-Portfolio  Manager  of  its  Seligman
International Growth Portfolio and Seligman Global Growth Portfolio.

The Emerging Markets Team,  headed by Mr. Daniel J. Barker,  will be responsible
for the  international  investments of the Emerging Markets Growth Fund. He is a
Vice  President of the  Corporation.  Mr. Barker joined  Seligman on October 11,
1999 as a Senior Vice  President.  Prior to joining  Seligman,  Mr. Barker was a
Portfolio  Manager  at GE  Investments  since  1994.  Prior  thereto,  he  was a
Corporate Financial Analyst at GE Information Services from 1990 to 1994.


<PAGE>

The Global  Technology Team, headed by Mr. Paul H. Wick, will be responsible for
the  international  investments  of the Global  Technology  Fund.  Mr.  Wick,  a
Managing  Director of Seligman,  is a Vice President of the  Corporation and has
been Co-Portfolio Manager of the Global Technology Fund since its inception. Mr.
Wick has been a Managing  Director of Seligman since January 1995 and a Director
of  Seligman  since  November  1997.  Mr.  Wick  has been a Vice  President  and
Portfolio  Manager of Seligman  Communications  and Information Fund, Inc. since
January 1990 and December 1989,  respectively.  Mr. Wick is a Vice President and
Co-Portfolio  Manager of Seligman New Technologies  Fund, Inc. He is also a Vice
President of Seligman  Portfolios,  Inc. and  Portfolio  Manager of its Seligman
Communications  and  Information  Portfolio  and  Co-Portfolio  Manager  of  its
Seligman Global Technology Portfolio.

Ms. Kei Yamamoto,  a Senior Vice President of Seligman,  is Co-Portfolio Manager
of the Global  Technology Fund. She is a Vice President of the Corporation.  Ms.
Yamamoto  joined  Seligman in May 1998 as a Vice President and has been a Senior
Vice President since January 2000. Prior to joining  Seligman,  Ms. Yamamoto was
an Associate  Portfolio Manager at Oppenheimer Funds, Inc. from 1997 to 1998 and
an Assistant  Portfolio  Manager at Franklin  Templeton Group from 1994 to 1997.
She is also a Vice  President  of Seligman  Portfolios,  Inc.  and  Co-Portfolio
Manager of its Seligman Global Technology Portfolio.

Mr.  Steven A. Werber,  a Vice  President of the  Corporation,  is  Co-Portfolio
Manager of the Global Technology Fund. Mr. Werber joined Seligman on January 10,
2000 as a Senior Vice President.  Prior to joining  Seligman,  Mr. Werber was an
Analyst and Portfolio Manager at Fidelity Investments  International since 1996.
Prior thereto,  he was an Associate at Goldman Sachs  International from 1992 to
1996.  Mr.  Werber is also a Vice  President  of Seligman  Portfolios,  Inc. and
Co-Portfolio Manager of its Seligman Global Technology Portfolio.

The Corporation has also removed  "Henderson" from its name, as well as from the
names of each of its five series. In addition,  the Seligman  International Fund
has changed its name to the "Seligman  International  Growth Fund," the Seligman
Global Growth  Opportunities  Fund has changed its name to the "Seligman  Global
Growth Fund," and the Seligman Emerging Markets Growth Fund has changed its name
to the "Seligman Emerging Markets Fund."

                                 _______________

The following supersedes the fourth full paragraph on page 22, under the Section
"Management of the Funds," in the Corporation's prospectus:

"Each Fund pays Seligman a fee for its management services equal to a percentage
of the Fund's average daily net assets. The fee rate declines as each Fund's net
assets  increase.  The management fee rate with respect to the Emerging  Markets
Fund is equal to 1.25% of  average  daily net  assets  on the first $1  billion,
1.15% of average  daily net  assets on the next $1 billion  and 1.05% of average
daily net assets in excess of $2 billion.  The  management fee rate with respect
to the  Global  Technology  Fund is equal to an annual  rate of 1.00% of average
daily net assets on the first $2  billion,  .95% of average  daily net assets on
the next $2  billion  and .90% of  average  daily  net  assets  in  excess of $4
billion.  The management fee rate with respect to each other Fund is equal to an
annual rate of 1.00% of average  daily net assets on the first $1 billion,  .95%
of average daily net assets on the next $1 billion and .90% of average daily net
assets in excess of $2 billion."

EQSHGS1-1/00


<PAGE>



                       Supplement, dated January 21, 2000,
         to the Statement of Additional Information, dated June 1, 1999
                                       of
              Seligman Global Fund Series, Inc. (the "Corporation")
             (formerly, Seligman Henderson Global Fund Series, Inc.)


The following supersedes the related information set forth in the Corporation's
statement of additional information.

On January 21, 2000,  pursuant to authorization from the Corporation's  Board of
Directors,  J. & W.  Seligman & Co.  Incorporated  ("Seligman"),  manager of the
Corporation,  gave notice to Henderson Investment Management Limited ("HIML") of
its intent to terminate the Subadvisory  Agreement  between Seligman and HIML in
respect of the Seligman  Henderson  International  Fund, the Seligman  Henderson
Emerging Markets Growth Fund, the Seligman Henderson Global Growth Opportunities
Fund, and the Seligman  Henderson Global  Technology Fund (the "Funds").  During
the notice  period,  HIML will  continue  to provide  the Funds with  investment
advice,  research  and  assistance  with  respect to their  non-US  investments,
subject to Seligman's  overall  supervision.  Following the close of business on
March  31,  2000,  Seligman  will  assume  full  responsibility  for the  non-US
investments of the Funds.

HIML will continue to act as subadvisor  with respect to the Seligman  Henderson
Global  Smaller  Companies  Fund and to receive a fee from Seligman based on the
"applicable  percentage" of the average monthly assets of the Smaller  Companies
Fund under its  supervision.  The  "applicable  percentage" is an annual rate of
0.90% for the period July 1, 1998 to June 30, 1999; 0.70% for the period July 1,
1999 to June 30, 2000; and 0.50% thereafter.

                                _______________

The Corporation has also removed  "Henderson" from its name, as well as from the
names of each of its five series. In addition,  the Seligman  International Fund
has changed its name to the "Seligman  International  Growth Fund," the Seligman
Global Growth  Opportunities  Fund has changed its name to the "Seligman  Global
Growth Fund," and the Seligman Emerging Markets Growth Fund has changed its name
to the "Seligman Emerging Markets Fund."


EQSHGS1-1/00




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