<PAGE>   1
                                                                     Exhibit 3.1



                          CERTIFICATE OF INCORPORATION

                                       OF

                           BELL TECHNOLOGY GROUP LTD.



         The undersigned, being of legal age, in order to form a corporation
under and pursuant to Section 101 et seq. of the General Corporation Law of the
State of Delaware, does hereby set forth as follows:


         FIRST, the name of the corporation is BELL TECHNOLOGY GROUP LTD. (the
"Company").


         SECOND, the address of the Company's registered office in the State of
Delaware is c/o United Corporate Services, Inc., 15 East North Street, in the
City of Dover, County of Kent, State of Delaware 19901 and the name of the
registered agent at said address is United Corporate Services, Inc.


         THIRD, the purpose of the Company is to engage in any lawful act or
activity for which corporations may be organized under the Delaware General
Corporation Law.


         FOURTH, the Company shall have the authority to issue ten million
(10,000,000) shares of Common Stock having a par value of $.01 per share. The
Company shall also have the authority to issue five hundred thousand (500,000)
shares of Preferred Stock having a par value of $.01 per share (the "Preferred
Shares"). The Board of Directors of the Company (the "Board") shall have the
right to authorize, by resolution of the Board adopted in accordance with the
by-laws of the Company, the issuance of the preferred shares of stock and, in
connection therewith, to (a) cause such shares to be issued in series; (b) the
annual rate of dividends payable with respect to the Preferred Shares or series
thereof; (c) the amounts payable upon redemption of the Preferred Shares; (d)
the amounts payable upon liquidation or dissolution of the Company; (e)
provisions as to voting, if any; and (f) such other rights, powers and
preferences as the Board shall determine.

         FIFTH, the name and mailing address of the incorporator of the Company
are:

                                    Marc H. Bell
                                    611 Broadway
                                    New York, NY 10012


         SIXTH, the Company shall fully indemnify any director of the Company
for monetary damages resulting from the breach of fiduciary duty as a director,
to the extent permitted by section 102(b)(7) of the Delaware General Corporation
Law; provided, however, that this provision shall not in any way eliminate or
limit the liability of any director (i) for any breach of the director's duty of
loyalty to the corporation or its stockholders, (ii) for acts or omissions not
in good faith or which involve intentional misconduct or a knowing violation of
law, (iii) under Section 174 of the Delaware General Corporation Law, (iv) for
any transaction from which the director derived an improper personal benefit.
<PAGE>   2
         SEVENTH, the Company reserves the right to amend, alter, change or
repeal any provision contained in this certificate of incorporation in the
manner now or hereafter prescribed by law, and all rights and powers conferred
herein on stockholders, directors and officers are subject to this reserved
power.


         IN WITNESS WHEREOF, the undersigned sets his name to this Certificate
of Incorporation and affirms that the statements made herein are true under the
penalties of perjury, this 28th day of September, 1995.





                                            /S/ Marc H. Bell             
                                            --------------------------
                                            Marc H. Bell, Incorporator
<PAGE>   3
                              CERTIFICATE OF MERGER
                                       OF
                          PFM TECHNOLOGIES CORPORATION
                                      INTO
                           BELL TECHNOLOGY GROUP LTD.

Pursuant to Section 252(c) of the State of Delaware General Corporation Law

         The undersigned, being the Surviving Corporation hereby sets forth as
follows:

         FIRST: The name of the Surviving Corporation is Bell Technology Group
Ltd.; its state of incorporation is the State of Delaware. The name of the
Non-Surviving Corporation is PFM Technologies Corporation; its state of
incorporation is the State of New York

         SECOND: An Agreement of Merger has been approved, adopted, certified,
executed and acknowledged by each constituent corporation in accordance with
Section 252 of the State of Delaware General Corporation Law.

         THIRD: The Certificate of Incorporation of Bell Technology Group Ltd.
shall be the Certificate of Incorporation of the Surviving~ Corporation.

         FOURTH: The executed Agreement of Merger is on file at the principal
place of business of the Surviving Corporation; the address of said principal
place of business is as follows:

                           Bell Technology Group Ltd.
                           611 Broadway, Suite 415
                           New York. NY 10012

         FIFTH: A copy of the Agreement of Merger will be furnished by the
Surviving Corporation, on request and without cost, to any stockholder of any
constituent corporation.

         SIXTH: The authorized capital stock of the Non-Surviving Corporation
which is incorporated under the laws of the State of New York is two hundred
shares having no par value.

         IN WITNESS WHEREOF, this certificate is hereby executed on this 28th
day of September, 1995.

         Bell Technology Group Ltd.


         By:  /S/ Marc H. Bell       
              ----------------
              Marc H. Bell, President
ATTEST:

/S/ Jennifer Spain       
------------------       
Jennifer Spain, Secretary
<PAGE>   4
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                           BELL TECHNOLOGY GROUP LTD.

         UNDER SECTION 242 OF THE DELAWARE GENERAL CORPORATION LAW

         BELL TECHNOLOGY GROUP LTD., a corporation organized and existing under
the laws of the State of Delaware (the "Corporation") hereby certifies as
follows:

1.    The name of the Corporation is Bell Technology Group Ltd.

2.    The Certificate of Incorporation of the Corporation was filed with the
      Secretary of State of Delaware, Division of Corporations on September 29,
      1995.

3.    The amendment of the Certificate of Incorporation of the Corporation
      effected by this Certificate of Amendment is to change the name of the
      Corporation and increase the number of shares authorized common stock of
      the corporation.

4.    To accomplish the foregoing amendment, Article FIRST of the Certificate of
      Incorporation of the Corporation, relating to the name of the Corporation,
      is hereby amended to read as follows:

                  "FIRST: The name of the Corporation is Globix Corporation.

5. Article FOURTH is hereby amended to read as follows:

                  "FOURTH: The Corporation shall have the authority to issue
         twenty million (20,000,000) shares of Common Stock having a par value
         of $.01 per share. The Corporation shall also have the authority to
         issue five hundred thousand (500,000) shares of Preferred Stock having
         a par value of $.01 per share (the "Preferred Shares"). The Board of
         Directors of the Corporation (the "Board") shall have the right to
         authorize, by resolution of the Board adopted in accordance with the
         By-laws of the Corporation, the issuance of the Preferred Shares and,
         in connection therewith, to (a) cause such shares to be issued in
         series; (b) fix the annual rate of dividends payable with respect to
         the Preferred shares or series thereof; (c) fix the amount payable upon
         redemption of the Preferred shares; (d) fix the amount payable upon
         liquidation or dissolution of the Company; (e) fix provisions as to
         voting rights, if any; and (e) fix such other rights, powers and
         preferences as the Board shall determine."

6.    The foregoing amendment of the Certificate of Incorporation of the
      Corporation was authorized by a vote of Board of Directors of the
      Corporation, followed by a vote of the holders of a majority of shares of
      the Corporation present at a meeting and entitled to vote on said
      amendment of the Certificate of Incorporation.
<PAGE>   5
7. The effective time of the amendment herein certified shall be June 1, 1998.

     IN WITNESS WHEREOF, we have subscribed this document on the date set forth
below and do hereby affirm, under the penalties of perjury, that the statements
contained herein have been examined by us and are true and correct.

May 8, 1998


                                                    /S/  Marc H. Bell    
                                                    -----------------    
                                                        Marc H. Bell, President

Attest:

    /S/ Paul Asher          
    --------------          
     Paul Asher, Secretary
<PAGE>   6
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                               GLOBIX CORPORATION

         UNDER SECTION 242 OF THE DELAWARE GENERAL CORPORATION LAW

GLOBIX CORPORATION, A CORPORATION ORGANIZED AND EXISTING UNDER THE LAWS OF THE
STATE OF DELAWARE (THE "CORPORATION") HEREBY CERTIFIES AS FOLLOWS:

1.    The name of the Corporation is Globix Corporation.

2.    The Certificate of Incorporation of the Corporation was filed with the
      Secretary of State of Delaware, Division of Corporations on September 29,
      1995 under the name Bell Technology Group Ltd.

3.    The amendment of the Certificate of Incorporation of the Corporation
      effected by this Certificate of Amendment is to increase the number of
      shares of authorized common stock of the corporation.

4.    To accomplish the foregoing amendment, Article FOURTH of the Certificate
      of Incorporation of the Corporation, is hereby amended to read as follows:

                  "FOURTH: The Corporation shall have the authority to issue
                  seventy-five million (75,000,000) shares of Common Stock
                  having a par value of $.01 per share. The Corporation shall
                  also have the authority to issue five hundred thousand
                  (500,000) shares of Preferred Stock having a par value of $.01
                  per share (the "Preferred Shares"). The Board of Directors of
                  the Corporation (the "Board") shall have the right to
                  authorize, by resolution of the Board adopted in accordance
                  with the By-laws of the Corporation, the issuance of the
                  Preferred Shares and, in connection therewith, to (a) cause
                  such shares to be issued in series; (b) fix the annual rate of
                  dividends payable with respect to the Preferred shares or
                  series thereof; (c) fix the amount payable upon redemption of
                  the Preferred shares; (d) fix the amount payable upon
                  liquidation or dissolution of the Company; (e) fix provisions
                  as to voting rights, if any; and (e) fix such other rights,
                  powers and preferences as the Board shall determine."

5.    The foregoing amendment of the Certificate of Incorporation of the
      Corporation was authorized by a vote of the Board of Directors of the
      Corporation, followed by a vote of the holders of a majority of all
      outstanding shares of the Corporation entitled to vote on said amendment
      of the Certificate of Incorporation.

     IN WITNESS WHEREOF, we have subscribed this document on the date set forth
below and do hereby affirm, under the penalties of perjury, that the statements
contained herein have been examined by us and are true and correct.

April 23, 1999


                                            By:     /s/ Marc H. Bell   
                                                 -------------------   
                                                 Marc H. Bell President

Attest:


By:     /s/ Paul Asher    
        --------------    
     Paul Asher, Secretary