EXHIBIT 32.1






             SECTION 1350 CERTIFICATION OF CHIEF EXECUTIVE OFFICER


         In connection with the Quarterly Report of Vector Group Ltd. (the
"Company") on Form 10-Q for the quarter ended June 30, 2004 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I,
Bennett S. LeBow, Chief Executive Officer of the Company, certify, pursuant to
18 U.S.C. section 1350, as adopted pursuant to section 906 of the
Sarbanes-Oxley Act of 2002, that, to my knowledge:

         1.       The Report 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 Report fairly presents, in
                  all material respects, the financial condition and results of
                  operations of the Company.



August 9, 2004


                                        /s/ Bennett S. LeBow
                                        ---------------------------------------
                                           Bennett S. LeBow
                                           Chairman and Chief Executive Officer