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                                                                   EXHIBIT 31.1

                                  CERTIFICATION


I, Peter K. Stevenson, certify that:

1. I have reviewed this Annual Report on Form 10-K/A of Globix Corporation for
the fiscal year ending September 30, 2004;

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 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.

5. The registrant's other certifying officer 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 controls 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.

Date: January 28, 2005                        GLOBIX CORPORATION


                                              /s/ Peter K. Stevenson
                                              ----------------------------------
                                              Peter K. Stevenson
                                              President, Chief Executive Officer