Supplement, dated April 2, 1998, to the prospectus, dated May 1, 1997,
                                    of
                  Seligman Portfolios, Inc. (the "Fund")
 

      The following  supersedes the related  information  set forth in the
Fund's prospectus.
 
      On March 30, 1998,  AMP Limited,  an Australian  life  insurance and
financial  services  company,  acquired  control of Henderson plc pursuant
to a cash offer.  Henderson  plc is the indirect  owner of 50% of Seligman
Henderson  Co., the  Subadviser  to the Seligman  Henderson  Portfolios of
the Fund.  As a result of this  acquisition,  the  subadvisory  agreements
between  the  Manager  and  Seligman  Henderson  Co.  relating to the Fund
terminated  automatically  in accordance with their terms.  Pursuant to an
order  issued by the  Securities  and  Exchange  Commission,  and with the
approval of the Fund's  Board of  Directors,  the Manager has entered into
new  subadvisory  agreements  with Seligman  Henderson Co. with respect to
the  Seligman  Henderson  Portfolios  of the  Fund.  The  new  subadvisory
agreements  are  identical  in  all  respects  to  the  previous
agreements  except  for  their   commencement  and  termination  dates.  A
meeting of shareholders of the Seligman  Henderson  Portfolios of the Fund
is  exepcted  to be held on June 30,  1998 to vote on the new  subadvisory
agreements.


SUPP3-4/98