EXHIBIT 99.1

                    CERTIFICATION OF CHIEF EXECUATIVE OFFICER
                              OF GLOBIX CORPORATION

         This certification is provided pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, and accompanies the
quarterly report on Form 10-Q (the "Form 10-Q") for the quarter ended March 31,
2003 of Globix Corporation ("the Company").

         I, Peter K. Stevenson, the Chief Executive Officer of the Company
certify that:

                  (i)      the Form 10-Q fully complies with the requirements of
                           Section 13(a) or Section 15(d) of the Securities
                           Exchange Act of 1934 (15 U.S.C. Section 78m(a) or
                           Section 780(d) ); 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.

Dated: May 15, 2003

                                                        /s/ Peter K. Stevenson
                                                        ------------------------
                                                        Name: Peter K. Stevenson

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