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                                                                    Exhibit 31.1

                                 CERTIFICATIONS

I, Peter K. Stevenson, certify that:

     1.  I have reviewed this Annual Report on Form 10-K of Globix Corporation
         for the fiscal year ending September 30, 2003;

     2.  Based on my knowledge, this Annual Report does not contain any untrue
         statement of a material fact or omit to state a material fact necessary
         to make the statements made, in light of the circumstances under which
         such statements were made, not misleading with respect to the period
         covered by this Annual Report;

     3.  Based on my knowledge, the financial statements, and other financial
         information included in this Annual Report, fairly present in all
         material respects the financial condition, results of operations and
         cash flows of the registrant as of, and for, the periods presented in
         this Annual Report;

     4.  The registrant's other certifying officer(s) and I are responsible for
         establishing and maintaining disclosure controls and procedures (as
         defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
         registrant and have:

            a.  Designed such disclosure controls and procedures, or caused such
                disclosure controls and procedures to be designed under our
                supervision, to ensure that material information relating to the
                registrant, including its consolidated subsidiaries, is made
                known to us by others within those entities, particularly during
                the period in which this Annual Report is being prepared;

            b.  Evaluated the effectiveness of the registrant's disclosure
                controls and procedures and presented in this Annual Report our
                conclusions about the effectiveness of the disclosure controls
                and procedures, as of the end of the period covered by this
                Annual Report based on such evaluation; and

            c.  Disclosed in this Annual Report any change in the registrant's
                internal control over financial reporting that occurred during
                the registrant's fourth fiscal quarter that has materially
                affected, or is reasonably likely to materially affect, the
                registrant's internal control over financial reporting; and

     5.  The registrant's other certifying officer(s) and I have disclosed,
         based on our most recent evaluation of internal control over financial
         reporting, to the registrant's auditors and the audit committee of the
         registrant's board of directors (or persons performing the equivalent
         functions):

            a.  All significant deficiencies and material weaknesses in the
                design or operation of internal control over financial reporting
                which are reasonably likely to adversely affect the registrant's
                ability to record, process, summarize and report financial
                information; and

            b.  Any fraud, whether or not material, that involves management or
                other employees who have a significant role in the registrant's
                internal control over financial reporting.

                                           Globix Corporation

Date: December 18, 2003                    /s/ Peter K. Stevenson
                                           ----------------------
                                           Peter K. Stevenson
                                           President and Chief Executive Officer