Helios Multi-Sector High Income Fund (XHMHX) N-CSRS Certified semi-annual shareholder report (management investment company)

EX-99.906CERT

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act

I, Brian B. Sullivan, President and Principal Executive Officer of RMK Multi-Sector High Income Fund, Inc. (the “Registrant”), certify that to my knowledge:

1. The Registrant’s periodic report on Form N-CSR for the period ended September 30, 2006 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

Date: December 6, 2006	By:	/s/ Brian B. Sullivan
		Brian B. Sullivan
		President and Principal Executive Officer

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act

I, J. Thompson Weller, Sr., Treasurer and Principal Financial Officer of RMK Multi-Sector High Income Fund, Inc. (the “Registrant”), certify that to my knowledge:

1. The Registrant’s periodic report on Form N-CSR for the period ended September 30, 2006 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

Date: December 6, 2006	By:	/s/ J. Thompson Weller, Sr.
		J. Thompson Weller, Sr.
		Treasurer and Principal Financial Officer