Exhibit 32.1

                           CERTIFICATION PURSUANT TO
                            18 U.S.C. SECTION 1350
                (SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002)

         In connection with the Quarterly Report of on Form 10-Q of Globix
Corporation (the "Company") for the period ending June 30, 2002 as filed with
the Securities and Exchange Commission (the "Report"), I, Peter K. Stevenson,
Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C.
Section 1350, that:

         (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 as of June 30, 2002 (the last date of
             the period covered by the Report).

                                       ----------------------------------------
                                       Peter K. Stevenson
                                       Chief Executive Officer

Date: September 8, 2003