<PAGE>   1
                                                                    EXHIBIT 3.11


                            CERTIFICATE OF AMENDMENT

                                     TO THE

                          CERTIFICATE OF INCORPORATION

                                       OF

                         GLOBAL TELESYSTEMS GROUP, INC.



         GLOBAL TELESYSTEMS GROUP, INC., a Delaware corporation, HEREBY
CERTIFIES AS FOLLOWS:

         1. The name of the corporation is Global TeleSystems Group, Inc. The
date of filing of its Certificate of Incorporation with the Secretary of State
of the State of Delaware was September 30, 1993.

         2. This Certificate of Amendment sets forth amendments to the
Certificate of Incorporation, as amended, of the Corporation that were duly
adopted by the written consent of the holders of a majority of the outstanding
stock of the Corporation entitled to vote thereon in accordance with the
provisions of Section 242 of the General Corporation Law of the State of
Delaware. Written notice of the taking of corporate action shall be given
promptly in accordance with the provisions of Section 228 of the General
Corporation Law of the State of Delaware.

         3. Article SIXTH of the Certificate of Incorporation, as amended, of
the Corporation is hereby amended to read in full as follows:

         "SIXTH: The Corporation 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 statute, and, except as
         provided in the next following sentence, all rights and powers
         conferred herein upon stockholders and directors are granted subject to
         this reservation. This Article Sixth and Articles Eleventh and Twelfth
         of this Certificate of Incorporation of the Corporation, each as
         amended, and notwithstanding the fact that a lesser percentage may be
         specified by law, may not be amended, altered, changed or repealed
         without the affirmative vote of the holders of at least seventy-five
         percent (75%) of the shares of capital stock of the Corporation issued
         and outstanding and entitled to vote."



                                       1
<PAGE>   2




         4. The Certificate of Incorporation of the Corporation, as amended, is
hereby amended by inserting a new Article TWELFTH as follows:

          "TWELFTH:  Stockholders of the Corporation may not take any action by
written consent in lieu of a meeting."

          IN WITNESS WHEREOF, GLOBAL TELESYSTEMS GROUP, INC. has caused this
certificate to be signed by Grier C. Raclin, its Senior Vice President, General
Counsel and Secretary, and attested by Arnold Y. Dean, its Assistant Secretary,
this 9th day of February, 1998.

                                GLOBAL TELESYSTEMS GROUP, INC.


                                By:    /s/ Grier C. Raclin
                                   ------------------------------------------
                                Name:  Grier C. Raclin
                                Title: Senior Vice President,
                                       General Counsel and Secretary
ATTEST:


By:      /s/ Arnold Y. Dean
   ----------------------------------
Name:    Arnold Y. Dean
Title:   Assistant Secretary

                                       2