SELIGMAN HENDERSON GLOBAL FUND SERIES INC
497, 1998-07-06
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     Supplement, dated July 2, 1998, to the prospectus, dated March 1, 1998
                                      of
           Seligman Henderson Global Fund Series, Inc. (the "Fund")


      The following information supersedes and replaces any contrary information
in the Fund's prospectus.

      On June 30, 1998, the  shareholders  of each series of the Fund approved a
Subadvisory  Agreement between the Manager and Henderson  Investment  Management
Limited (the "New Subadviser").  The Fund's prior subadvisory  arrangements with
Seligman  Henderson Co. terminated on June 30, 1998. The Subadvisory  Agreement,
which became  effective on July 1, 1998,  provides that the New Subadviser  will
furnish  investment  advice,  research and  assistance  with respect to the each
series'  non-U.S.  investments.  The Manager shall be  responsible  for any U.S.
investments and has overall responsibility for the management of the Fund.

      The New  Subadviser,  a wholly  owned  subsidiary  of  Henderson  plc,  is
headquartered  in the  United  Kingdom.  Henderson  plc is a  subsidiary  of AMP
Limited, an Australian life insurance and financial services company.  Under the
new arrangements, the same personnel who provided investment management services
to the Fund on behalf of Seligman  Henderson  Co., the prior  subadviser,  shall
continue to do so.

      The New  Subadviser  receives a fee from the  Manager,  in respect of each
series,  based on the  "applicable  percentage" of the average monthly assets of
such series under the New Subadviser's 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
Subadvisory  Agreement  provides that it will continue  until  December 31, 1999
and,  thereafter,  is  subject  to the annual  approval  of the Fund's  Board of
Directors.

      The subadvisory  fee under these  arrangements is paid by the Manager from
its own  management  fee and will not increase the fees payable by any series of
the Fund.


EQSHGS-3-7/98

<PAGE>


                     Supplement, dated July 2, 1998, to the
           Statement of Additional Information, dated March 1, 1998
                                       of
           Seligman Henderson Global Fund Series, Inc. (the "Fund")

      The following information supersedes and replaces any contrary information
in the Fund's Statement of Additional Information.

      On June 30, 1998, the  shareholders  of each series of the Fund approved a
Subadvisory  Agreement between the Manager and Henderson  Investment  Management
Limited (the "New Subadviser").  The Fund's prior subadvisory  arrangements with
Seligman  Henderson Co. terminated on June 30, 1998. The Subadvisory  Agreement,
which became  effective on July 1, 1998,  provides that the New Subadviser  will
furnish  investment  advice,  research and  assistance  with respect to the each
series'  non-U.S.  investments.  The Manager shall be  responsible  for any U.S.
investments and has overall responsibility for the management of the Fund.

      The New  Subadviser,  a wholly  owned  subsidiary  of  Henderson  plc,  is
headquartered  in the  United  Kingdom.  Henderson  plc is a  subsidiary  of AMP
Limited, an Australian life insurance and financial services company.  Under the
new arrangements, the same personnel who provided investment management services
to the Fund on behalf of Seligman  Henderson  Co., the prior  subadviser,  shall
continue to do so.

      The New  Subadviser  receives a fee from the  Manager,  in respect of each
series,  based on the  "applicable  percentage" of the average monthly assets of
such series under the New Subadviser's 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
Subadvisory  Agreement  provides that it will continue  until  December 31, 1999
and,  thereafter,  is  subject  to the annual  approval  of the Fund's  Board of
Directors.

      The subadvisory  fee under these  arrangements is paid by the Manager from
its own  management  fee and will not increase the fees payable by any series of
the Fund.

EQSHGS-3-7/98



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