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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 June 30, 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: August 3, 2004
                                           /s/ Peter K. Stevenson
                                           -------------------------------------
                                           Peter K. Stevenson
                                           President and Chief Executive Officer