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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 of Globix
          Corporation for the fiscal quarter ending December 31, 2004;

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


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