EX-99.906CERT


                                 EXHIBIT 12 (b)
                           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 annual report on Form N-CSR of the Registrant for the fiscal year
         ended December 31, 2004 (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.

Date:  March 8, 2005                /s/ BRIAN T. ZINO
                                    -----------------------------
                                    Brian T. Zino
                                    Chief Executive Officer





Date:  March 8, 2005                /s/ LAWRENCE P. VOGEL
                                    -----------------------------
                                    Lawrence P. Vogel
                                    Chief Financial Officer