**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, 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: August
                  15, 2005
                By:
                /s/ Peter
                  K. StevensonPeter
                    K. Stevenson
                  President
                    andChief
                    Executive Officer