EXHIBIT 12 (b)
                                  EX-99.906CERT
                           RULE 30a-2(b) CERTIFICATION



     Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a)
and (b) of section 1350, chapter 63 of title 18, United States Code), each of
the undersigned officers of Seligman High Income Fund Series (the "registrant"),
do hereby certify, to such officer's knowledge, that:

     (1)  The semi-annual Report on Form N-CSR of the registrant for the six
          months ended June 30, 2005 (the "Form N-CSR") fully complies with the
          requirements of Section 13(a) or 15(d) of the Securities Exchange Act
          of 1934; and

     (2)  the information contained in the Form N-CSR fairly presents, in all
          material respects, the financial condition and results of operations
          of the registrant.


                           By:      /S/ BRIAN T. ZINO
                                    -----------------
                                    Brian T. Zino
                                    Chief Executive Officer

                           Date: September 7, 2005



                           By:      /S/ LAWRENCE P. VOGEL
                                    ---------------------
                                    Lawrence P. Vogel
                                    Chief Financial Officer

                           Date: September 7, 2005