<PAGE>   1


                           CERTIFICATE OF DESIGNATION
                       OF THE VOTING POWERS, DESIGNATION,
                    PREFERENCES AND RELATIVE, PARTICIPATING,
              OPTIONAL OR OTHER SPECIAL RIGHTS AND QUALIFICATIONS,
                      LIMITATIONS AND RESTRICTIONS OF THE
                            SERIES A PREFERRED STOCK

                      -----------------------------------

                         Pursuant to Section 151 of the
                           General Corporation Law of
                             the State of Delaware

                      -----------------------------------


                 I, Grier Raclin, Senior Vice President, General Counsel and
Secretary of Global TeleSystems Group, Inc., a corporation organized and
existing under the General Corporation Law of the State of Delaware (the
"Corporation"), DO HEREBY CERTIFY:

                 that, pursuant to authority conferred upon the Board of
Directors of the Corporation by its Certificate of Incorporation (the
"Certificate") and delegated to a committee of the Board of Directors of the
Corporation at a duly called meeting held on December 5, 1997, at which a
quorum was present and acted throughout, and, pursuant to the provisions of
Section 151 of the General Corporation Law of the State of Delaware, said
committee acting by unanimous written consent on January 30, 1998, adopted the
following resolutions, which resolutions remain in full force and effect on the
date hereof, creating a series of 200,000 shares of Preferred Stock having a
par value of $.0001 per share, designated as Series A Preferred Stock (the
"Series A Preferred Stock") out of the authorized preferred stock, par value of
$.0001 per share (the "Preferred Stock"):

                 RESOLVED, that pursuant to the authority vested in this
committee of the Board of Directors in accordance with the provisions of the
Certificate and resolutions of the Board or Directors duly adopted on December
5, 1997, this committee of the Board of Directors does hereby create, authorize
and provide for the issuance of the Series A Preferred Stock having the voting
powers, designation, relative, participating, optional and other special
rights, preferences, and qualifications, limitations and restrictions thereof
that are set forth as follows:

                 Section 1.  Designation and Amount.  The shares of such series
shall be designated as "Series A Preferred Stock" and the number of shares
constituting such series shall be 200,000.

                 Section 2.  Dividends and Distributions.  (A)  Subject to the
prior and superior rights of the holders of any shares of any other series of
Preferred Stock or any other shares of
<PAGE>   2
                                       2

preferred stock of the Corporation ranking prior and superior to the shares of
Series A Preferred Stock with respect to dividends, each holder of one
one-thousandth (1/1,000) of a share (a "Unit") of Series A Preferred Stock
shall be entitled to receive, when, as and if declared by the Board of
Directors out of funds legally available for that purpose, (i) quarterly
dividends payable in cash on the last day of March, June, September and
December in each year (each such date being a "Quarterly Dividend Payment
Date"), commencing on the first Quarterly Dividend Payment Date after the first
issuance of such Unit of Series A Preferred Stock, in an amount per Unit
(rounded to the nearest cent) equal to the greater of (a) $.01 or (b) subject
to the provision for adjustment hereinafter set forth, the aggregate per share
amount of all cash dividends declared on shares of the Common Stock since the
immediately preceding Quarterly Dividend Payment Date, or, with respect to the
first Quarterly Dividend Payment Date, since the first issuance of a Unit of
Series A Preferred Stock, and (ii) subject to the provision for adjustment
hereinafter set forth, quarterly distributions (payable in kind) on each
Quarterly Dividend Payment Date in an amount per Unit equal to the aggregate
per share amount of all non-cash dividends or other distributions (other than a
dividend payable in shares of Common Stock or a subdivision of the outstanding
shares of Common Stock, by reclassification or otherwise) declared on shares of
Common Stock since the immediately preceding Quarterly Dividend Payment Date,
or with respect to the first Quarterly Dividend Payment Date, since the first
issuance of a Unit of Series A Preferred Stock.  In the event that the
Corporation shall at any time after February 2, 1998 (the "Rights Declaration
Date") (i) declare any dividend on outstanding shares of Common Stock payable
in shares of Common Stock, (ii) subdivide outstanding shares of Common Stock or
(iii) combine outstanding shares of Common Stock into a smaller number of
shares, then in each such case the amount to which the holder of a Unit of
Series A Preferred Stock was entitled immediately prior to such event pursuant
to the preceding sentence shall be adjusted by multiplying such amount by a
fraction the numerator of which shall be the number of shares of Common Stock
that are outstanding immediately after such event and the denominator of which
shall be the number of shares of Common Stock that were outstanding immediately
prior to such event.

                 (B)      The Corporation shall declare a dividend or
distribution on Units of Series A Preferred Stock as provided in paragraph (A)
above immediately after it declares a dividend or distribution on the shares of
Common Stock (other than a dividend payable in shares of Common Stock);
provided, however, that, in the event no dividend or distribution shall have
been declared on the Common Stock during the period between any Quarterly
Dividend Payment Date and the next subsequent Quarterly Dividend Payment Date,
a dividend of $0.01 per Unit on the Series A Preferred Stock shall nevertheless
be payable on such subsequent Quarterly Dividend Payment Date.

                 (C)      Dividends shall begin to accrue and shall be
cumulative on each outstanding Unit of Series A Preferred Stock from the
Quarterly Dividend Payment Date next preceding the date of issuance of such
Unit of Series A Preferred Stock, unless the date of issuance of such  Unit is
prior to the record date for the first Quarterly Dividend Payment Date, in
which case, dividends on such Unit shall begin to accrue from the date of
issuance of such
<PAGE>   3
                                       3

Unit, or unless the date of issuance is a Quarterly Dividend Payment Date or is
a date after the record date for the determination of holders of Units of
Series A Preferred Stock entitled to receive a quarterly dividend and before
such Quarterly Dividend Payment Date, in either of which events such dividends
shall begin to accrue and be cumulative from such Quarterly Dividend Payment
Date.  Accrued but unpaid dividends shall not bear interest. Dividends paid on
Units of Series A Preferred Stock in an amount less than the aggregate amount
of all such dividends at the time accrued and payable on such Units shall be
allocated pro rata on a unit-by-unit basis among all Units of Series A
Preferred Stock at the time outstanding.  The Board of Directors may fix a
record date for the determination of holders of Units of Series A Preferred
Stock entitled to receive payment of a dividend or distribution declared
thereon, which record date shall be no more than 30 days prior to the date
fixed for the payment thereof.

                 Section 3.  Voting Rights.  The holders of Units of Series A
Preferred Stock shall have the following voting rights:

         (A)     Subject to the provision for adjustment hereinafter set forth,
each Unit of Series A Preferred Stock shall entitle the holder thereof to one
vote on all matters submitted to a vote of the stockholders of the Corporation.
In the event the Corporation shall at any time after the Rights Declaration
Date (i) declare any dividend on outstanding shares of Common Stock payable in
shares of Common Stock, (ii) subdivide outstanding shares of Common Stock or
(iii) combine the outstanding shares of Common Stock into a smaller number of
shares, then in each such case the number of votes per Unit to which holders of
Units of Series A Preferred Stock were entitled immediately prior to such event
shall be adjusted by multiplying such number by a fraction the numerator of
which shall be the number of shares of Common Stock outstanding immediately
after such event and the denominator of which shall be the number of shares of
Common Stock that were outstanding immediately prior to such event.

         (B)     Except as otherwise provided herein or by law, the holders of
Units of Series A Preferred Stock and the holders of shares of Common Stock
shall vote together as one class on all matters submitted to a vote of
stockholders of the Corporation.

         (C)     (i)  If at any time dividends on any Units of Series A
Preferred Stock shall be in arrears in an amount equal to six quarterly
dividends thereon, then during the period (a "default period") from the
occurrence of such event until such time as all accrued and unpaid dividends
for all previous quarterly dividend periods and for the current quarterly
dividend period on all Units of Series A Preferred Stock then outstanding shall
have been declared and paid or set apart for payment, all holders of Units of
Series A Preferred Stock, voting separately as a class, shall have the right to
elect two Directors.

         (ii)  During any default period, such voting rights of the holders of
Units of Series A Preferred Stock may be exercised initially at a special
meeting called pursuant to subparagraph (iii) of this Section 3(C) or at any
annual meeting of stockholders, and thereafter at annual
<PAGE>   4
                                       4

meetings of stockholders, provided that neither such voting rights nor any
right of the holders of Units of Series A Preferred Stock to increase, in
certain cases, the authorized number of Directors may be exercised at any
meeting unless one-third of the outstanding Units of Preferred Stock shall be
present at such meeting in person or by proxy.  The absence of a quorum of the
holders of Common Stock shall not affect the exercise by the holders of Units
of Series A Preferred Stock of such rights.  At any meeting at which the
holders of Units of Series A Preferred Stock shall exercise such voting rights
initially during an existing default period, they shall have the right, voting
separately as a class, to elect Directors to fill up to two vacancies in the
Board of Directors, if any such vacancies may then exist, or, if such right is
exercised at an annual meeting, to elect two Directors.  If the number which
may be so elected at any special meeting does not amount to the required
number, the holders of the Series A Preferred Stock shall have the right to
make such increase in the number of Directors as shall be necessary to permit
the election by them of the required number.  After the holders of Units of
Series A Preferred Stock shall have exercised their right to elect Directors
during any default period, the number of Directors shall not be increased or
decreased except as approved by a vote of the holders of Units of Series A
Preferred Stock as herein provided or pursuant to the rights of any equity
securities ranking senior to the Series A Preferred Stock.

         (iii)  Unless the holders of Series A Preferred Stock shall, during an
existing default period, have previously exercised their right to elect
Directors, the Board of Directors may order, or any stockholder or stockholders
owning in the aggregate not less than 25% of the total number of the Units of
Series A Preferred Stock outstanding may request, the calling of a special
meeting of the holders of Units of Series A Preferred Stock, which meeting
shall thereupon be called by the Secretary of the Corporation.  Notice of such
meeting and of any annual meeting at which holders of Units of Series A
Preferred Stock are entitled to vote pursuant to this paragraph (C)(iii) shall
be given to each holder of record of Units of Series A Preferred Stock by
mailing a copy of such notice to him at his last address as the same appears on
the books of the Corporation.  Such meeting shall be called for a time not
earlier than 20 days and not later then 60 days after such order or request or
in default of the calling of such meeting within 60 days after such order or
request, such meeting may be called on similar notice by any stockholder or
stockholders owning in the aggregate not less than 25% of the total number of
outstanding Units of Series A Preferred Stock.  Notwithstanding the provisions
of this paragraph (C)(iii), no such special meeting shall be called during the
60 days immediately preceding the date fixed for the next annual meeting of the
stockholders.

         (iv)  During any default period, the holders of shares of Common Stock
and Units of Series A Preferred Stock, and other classes or series of stock of
the Corporation, if applicable, shall continue to be entitled to elect all the
Directors until holders of the Units of Series A Preferred Stock shall have
exercised their right to elect two Directors voting as a separate class, after
the exercise of which right (x) the Directors so elected by the holders of
Units of Series A Preferred Stock shall continue in office until their
successors shall have been elected by such holders or until the expiration of
the default period, and (y) any vacancy in the Board of Directors may (except
as provided in paragraph (C)(ii) of this Section 3) be filled by vote of
<PAGE>   5
                                       5

a majority of the remaining Directors theretofore elected by the holders of the
class of capital stock which elected the Director whose office shall have
become vacant.  References in this paragraph (C) to Directors elected by the
holders of a particular class of capital stock shall include Directors elected
by such Directors to fill vacancies as provided in clause (y) of the foregoing
sentence.

         (v)  Immediately upon the expiration of a default period, (x) the
right of the holders of Units of Series A Preferred Stock as a separate class
to elect Directors shall cease, (y) the term of any Directors elected by the
holders of Units of Series A Preferred Stock as a separate class shall
terminate, and (z) the number of Directors shall be such number as may be
provided for in the Certificate or by-laws irrespective of any increase made
pursuant to the provisions of paragraph (C)(ii) of this Section 3 (such number
being subject, however, to change thereafter in any manner provided by law or
in the Certificate or by-laws).  Any vacancies in the Board of Directors
effected by the provisions of clauses (y) and (z) in the preceding sentence may
be filled by a majority of the remaining Directors.

         (vi)  The provisions of this paragraph (C) shall govern the election
of Directors by holders of Units of Preferred Stock during any default period
notwithstanding any provisions of the Certificate to the contrary.

                 (D)      Except as set forth herein, holders of Units of
Series A Preferred Stock shall have no special voting rights and their consents
shall not be required (except to the extent they are entitled to vote with
holders of shares of Common Stock as set forth herein) for taking any corporate
action.

                 Section 4.  Certain Restrictions.  (A)  Whenever quarterly
dividends or other dividends or distributions payable on Units of Series A
Preferred Stock as provided in Section 2 are in arrears, thereafter and until
all accrued and unpaid dividends and distributions, whether or not declared, on
outstanding Units of Series A Preferred Stock shall have been paid in full, the
Corporation shall not

                 (i)  declare or pay dividends on, make any other distributions
         on, or redeem or purchase or otherwise acquire for consideration any
         shares of junior stock;

                 (ii)  declare or pay dividends on or make any other
         distributions on any shares of parity stock, except dividends paid
         ratably on Units of Series A Preferred Stock and shares of all such
         parity stock on which dividends are payable or in arrears in
         proportion to the total amounts to which the holders of such Units and
         all such shares are then entitled;

                 (iii)  redeem or purchase or otherwise acquire for
         consideration shares of any parity stock, provided, however, that the
         Corporation may at any time redeem, purchase or otherwise acquire
         shares of any such parity stock in exchange for shares of
<PAGE>   6
                                       6

         any junior stock;

                 (iv) purchase or otherwise acquire for consideration any Units
         of Series A Preferred Stock, except in accordance with a purchase
         offer made in writing or by publication (as determined by the Board of
         Directors) to all holders of such Units.

                 (B)      The Corporation shall not permit any subsidiary of
the Corporation to purchase or otherwise acquire for consideration any shares
of stock of the Corporation unless the Corporation could, under paragraph (A)
of this Section 4, purchase or otherwise acquire such shares at such time and
in such manner.

                 Section 5.  Reacquired Shares.  Any Units of Series A
Preferred Stock purchased or otherwise acquired by the Corporation in any
manner whatsoever shall be retired and cancelled promptly after the acquisition
thereof.  All such Units shall, upon their cancellation, become authorized but
unissued Units of Preferred Stock and may be reissued as part of a new series
of Preferred Stock to be created by resolution or resolutions of the Board of
Directors, subject to the conditions and restrictions on issuance set forth
herein.

                 Section 6.  Liquidation, Dissolution or Winding Up.  (A)  Upon
any voluntary or involuntary liquidation, dissolution or winding up of the
Corporation, no distribution shall be made (i) to the holders of shares of
junior stock unless the holders of Units of Series A Preferred Stock shall have
received, subject to adjustment as hereinafter provided in paragraph (B), the
greater of either (a) $0.01 per Unit plus an amount equal to accrued and unpaid
dividends and distributions thereon, whether or not earned or declared, to the
date of such payment, or (b) the amount equal to the aggregate per share amount
to be distributed to holders of shares of Common Stock, or (ii) to the holders
of shares of parity stock, unless simultaneously therewith distributions are
made ratably on Units of Series A Preferred Stock and all other shares of such
parity stock in proportion to the total amounts to which the holders of Units
of Series A Preferred Stock are entitled under clause (i)(a) of this sentence
and to which the holders of shares of such parity stock are entitled, in each
case upon such liquidation, dissolution or winding up.

                 (B)      In the event the Corporation shall at any time after
the Rights Declaration Date (i) declare any dividend on outstanding shares of
Common Stock payable in shares of Common Stock, (ii) subdivide outstanding
shares of Common Stock, or (iii) combine outstanding shares of Common Stock
into a smaller number of shares, then in each such case the aggregate amount to
which holders of Units of Series A Preferred Stock were entitled immediately
prior to such event pursuant to clause (i)(b) of paragraph (A) of this Section
6 shall be adjusted by multiplying such amount by a fraction the numerator of
which shall be the number of shares of Common Stock that are outstanding
immediately after such event and the denominator of which shall be the number
of shares of Common Stock that were outstanding immediately prior to such
event.
<PAGE>   7
                                       7


                 Section 7.  Consolidation, Merger, etc.  In case the
Corporation shall enter into any consolidation, merger, combination or other
transaction in which the shares of common stock are exchanged for or converted
into other stock or securities, cash and/or any other property, then in any
such case Units of Series A Preferred Stock shall at the same time be similarly
exchanged for or converted into an amount per Unit (subject to the provision
for adjustment hereinafter set forth) equal to the aggregate amount of stock,
securities, cash and/or any other property (payable in kind), as the case may
be, into which or for which each share of Common Stock is converted or
exchanged.  In the event the Corporation shall at any time after the Rights
Declaration Date (i) declare any dividend on outstanding shares of Common Stock
payable in shares of Common Stock, (ii) subdivide outstanding shares of Common
Stock, or (iii) combine outstanding Common Stock into a smaller number of
shares, then in each such case the amount set forth in the immediately
preceding sentence with respect to the exchange or conversion of Units of
Series A Preferred Stock shall be adjusted by multiplying such amount by a
fraction the numerator of which shall be the number of shares of Common Stock
that are outstanding immediately after such event and the denominator of which
shall be the number of shares of Common Stock that were outstanding immediately
prior to such event.

                 Section 8.  Redemption.  The Units of Series A Preferred Stock
shall not be redeemable.

                 Section 9.  Ranking.  The Units of Series A Preferred Stock
shall rank junior to all other series of the Preferred Stock and to any other
class of preferred stock that hereafter may be issued by the Corporation as to
the payment of dividends and the distribution of assets, unless the terms of
any such series or class shall provide otherwise.

                 Section 10.  Amendment.  The Certificate, including, without
limitation, this resolution, shall not hereafter be amended, either directly or
indirectly, or through merger or consolidation with another corporations in any
manner that would alter or change the powers, preferences or special rights of
the Series A Preferred Stock so as to affect them adversely without the
affirmative vote of the holders of a majority or more of the outstanding Units
of Series A Preferred Stock, voting separately as a class.

                 Section 11.  Fractional Shares.  The Series A Preferred Stock
may be issued in Units or other fractions of a share, which Units or fractions
shall entitle the holder, in proportion to such holder's fractional shares, to
exercise voting rights, receive dividends, participate in distributions and to
have the benefit of all other rights of holders of Series A Preferred Stock.

                 Section 12.  Certain Definitions.  As used herein with respect
to the Series A Preferred Stock, the following terms shall have the following
meanings:

                 (A)      The term "Common Stock" shall mean the class of stock
designated as the common stock, par value $0.10 per share, of the Corporation
at the date hereof or any
<PAGE>   8
                                       8

other class of stock resulting from successive changes or reclassification of
such common stock.

                 (B)      The term "junior stock" (i) as used in Section 4,
shall mean the Common Stock and any other class or series of capital stock of
the Corporation hereafter authorized or issued over which the Series A
Preferred Stock has preference or priority as to the payment of dividends and
(ii) as used in Section 6, shall mean the Common Stock and any other class or
series of capital stock of the Corporation over which the Series A Preferred
Stock has preference or priority in the distribution of assets on any
liquidation, dissolution or winding up of the Corporation.

                 (C)      The term "parity stock" (i) as used in Section 4,
shall mean any class or series of stock of the Corporation hereafter authorized
or issued ranking pari passu with the Series A Preferred Stock as to the
payment of dividends and (ii) as used in Section 6, shall mean any class or
series of capital stock ranking pari passu with the Series A Preferred Stock in
the distribution of assets on any liquidation, dissolution or winding up of the
Corporation.
<PAGE>   9
                                       9


                 IN WITNESS WHEREOF, Global TeleSystems Group, Inc. has caused
this Certificate to be signed by its Senior Vice President, General Counsel and
Secretary and attested by its Secretary this 2nd 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