Exhibit 32

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

In connection with the accompanying Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2004, I, Collin J. D’Silva, Chairman of the Board, President and Chief Executive Officer of Transgenomic, Inc., hereby certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, that:

(1) such Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2004, 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 such Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2004, fairly presents, in all material respects, the financial condition and results of operations of Transgenomic, Inc.

/s/    COLLIN J. D’SILVA        

Collin J. D’Silva

Chairman of the Board, President and

Chief Executive Officer

Date: April 14, 2005

A signed original of the certification required by Section 906 has been provided to Transgenomic, Inc. and will be retained by Transgenomic, Inc and furnished to the Securities and Exchange Commission or its staff upon request.

Exhibit 32

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

In connection with the accompanying Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2005, I, Michael A. Summers, Chief Financial Officer of Transgenomic, Inc., hereby certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, that:

(1) such Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2004, 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 such Annual Report on Form 10-K of Transgenomic, Inc. for the year ended December 31, 2004, fairly presents, in all material respects, the financial condition and results of operations of Transgenomic, Inc.

/s/    MICHAEL A. SUMMERS        

Michael A. Summers

Chief Financial Officer

Date: April 14, 2005

A signed original of the certification required by Section 906 has been provided to Transgenomic, Inc. and will be retained by Transgenomic, Inc and furnished to the Securities and Exchange Commission or its staff upon request.