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, 2006 (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: August 30, 2006
| /S/ BRIAN T. ZINO | ||
| Brian T. Zino | ||
| Chief Executive Officer |
| /S/ LAWRENCE P. VOGEL | ||
| Lawrence P. Vogel | ||
| Chief Financial Officer |