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 year ended December 31, 2008 (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/ PATRICK T. BANNIGAN | |
| Patrick T. Bannigan | ||
| Chief Executive Officer | ||
| Date: | March 9, 2009 | |
| By: | /S/ LAWRENCE P.VOGEL | |
| Lawrence P. Vogel | ||
| Chief Financial Officer | ||
| Date: | March 9, 2009 | |