EXHIBIT 32.1


                            CERTIFICATION PURSUANT TO
                 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


     In connection with the Quarterly Report of Globix Corporation (the
"Company") on Form 10-Q for the fiscal quarter ending December 31, 2004 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, as adopted pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002, 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.



Date: February 14, 2005
                                                 /s/ Peter K. Stevenson
                                                 -----------------------
                                                 Peter K. Stevenson
                                                 Chief Executive Officer


                                       22