Supplement, dated July 2, 1998, to the prospectus, dated May 1, 1998
                                       of
                     Seligman Portfolios, 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 of the  Seligman  Henderson
Portfolios 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  Seligman  Henderson   Portfolios'   non-U.S.
investments.  The Manager shall be responsible for any U.S.  investments and has
overall responsibility for the management of the Portfolios.

      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 for its services,  in respect of each Seligman
Henderson Portfolio, a monthly fee from the Manager. The fee is calculated at an
annual rate of 0.50% of each  Portfolio's  average  monthly assets under the New
Subadviser's  supervision.  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 Portfolio.

PORT1-7/98





                     Supplement, dated July 2, 1998, to the
            Statement of Additional Information, dated May 1, 1998
                                       of
                     Seligman Portfolios, 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 of the  Seligman  Henderson
Portfolios 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  Seligman  Henderson   Portfolios'   non-U.S.
investments.  The Manager shall be responsible for any U.S.  investments and has
overall responsibility for the management of the Portfolios.

      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 for its services,  in respect of each Seligman
Henderson Portfolio, a monthly fee from the Manager. The fee is calculated at an
annual rate of 0.50% of each  Portfolio's  average  monthly assets under the New
Subadviser's  supervision.  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 Portfolio.

PORT1-7/98