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 24