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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 March 31, 2005.

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: May 13, 2005
                             /s/ Peter K. Stevenson
                             -------------------------------------
                             Peter K. Stevenson
                             President and Chief Executive Officer