EXHIBIT 32.02 SECTION 906 CERTIFICATION CERTIFICATION PURSUANT TO SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE I, Stanley J. Talbi, the Chief Financial Officer of The Travelers Insurance Company (the "Company"), certify that (i) the Company's Quarterly Report on Form 10-Q for the quarter ended June 30, 2005 (the "Form 10-Q") fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company. Date: August 12, 2005 By: /s/ Stanley J. Talbi ------------------------------------ Stanley J. Talbi Senior Vice President and Chief Financial Officer A signed original of this written statement required by Section 906 has been provided to The Travelers Insurance Company and will be retained by The Travelers Insurance Company and furnished to the Securities and Exchange Commission or its staff upon request. 34