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                                                                    Exhibit 31.1
                                 CERTIFICATIONS


I, Peter K. Stevenson, certify that:

         1.       I have reviewed this Quarterly Report on Form 10-Q/A of Globix
                  Corporation for the fiscal quarter ending December 31, 2003;

         2.       Based on my knowledge, this Quarterly 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
                  Quarterly Report;

         3.       Based on my knowledge, the financial statements, and other
                  financial information included in this Quarterly 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
                  Quarterly 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
                           Quarterly Report is being prepared;

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

                  c.       Disclosed in this Quarterly Report any change in the
                           registrant's internal control over financial
                           reporting that occurred during the registrant's most
                           recent 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:  January 14, 2005

                                          /S/ Peter K. Stevenson
                                          --------------------------------------
                                          Peter K. Stevenson
                                          President and Chief Executive Officer