<PAGE>

                                                                   EXHIBIT 10.64
                         EQUALNET COMMUNICATIONS CORP.

          STATEMENT OF RESOLUTION OF BOARD OF
          DIRECTORS ESTABLISHING AND DESIGNATING
          SERIES E JUNIOR PREFERRED STOCK AND
          FIXING THE RIGHTS AND PREFERENCES OF
          SUCH SERIES

                             _____________________

TO THE SECRETARY OF STATE
   OF THE STATE OF TEXAS:

          Equalnet Communications Corp., pursuant to the provisions of Articles
2.13 and 2.19B of the Texas Business Corporation Act, submits the following
statement for the purpose of establishing and designating a series of shares and
fixing and determining the relative rights and preferences thereof:

          1.  The name of the Corporation is Equalnet Communications Corp.

          2.  The following is a true and correct copy of an extract from the
minutes of a meeting of the Board of Directors of the Corporation held on May
24, 1999, and includes a true and correct copy of certain resolutions duly
adopted  thereat.

          RESOLVED, that pursuant to authority vested in the Board of Directors
by the Articles of Incorporation of the Corporation, the Board of Directors does
hereby provide that the Statement of Resolution of Board of Directors
Establishing and Designating Series E Junior Preferred Stock and Fixing the
Rights and Preferences of Such Series is as follows:

                        SERIES E JUNIOR PREFERRED STOCK


          Section 1.  Designation and Amount.  The shares of such series shall
                      ----------------------
be designated as "Series E Junior Preferred Stock", and the number of shares
constituting the Series E Junior Preferred Stock shall be 900,000, and shall not
be subject to increase.

          Section 2.  Series E Preferred Stock Capital.  The amount to be
                      --------------------------------
represented in the Series E Convertible Preferred Stock capital of the
Corporation at all times for each outstanding share of Series E Junior Preferred
Stock shall be $0.01 per share.  The Corporation shall take such action as may
be required to maintain the amount required by this Section 3 to be represented
in stated capital for the Series E Junior Preferred Stock capital not less
frequently than monthly.
<PAGE>

          Section 3.  Rank.  All Series E Junior Preferred Stock shall rank (i)
                      ----
senior to the Common Stock, now or hereafter issued, as to distribution of
assets upon liquidation, dissolution, or winding up of the Corporation, whether
voluntary or involuntary, (ii) junior to the Series A Convertible Preferred
Stock, Series B Senior Convertible Preferred Stock, Series C Convertible
Preferred Stock and Series D Convertible Preferred Stock of the Corporation, as
to distributions of assets upon liquidation, dissolution, or winding up of the
Corporation, whether voluntary or involuntary and (iii) senior to any additional
series of the class of Preferred Stock which series the Board of Directors may
from time to time authorize and any additional class of preferred stock (or
series of preferred stock of such class) which the Board of Directors or the
stockholders may from time to time authorize in accordance herewith.

          Section 4.  Dividends and Distributions.  (a) The holders of shares of
                      ---------------------------
Series  E Junior  Preferred Stock shall not  be entitled to receive dividends.

          Section 5.  Liquidation Preference.  In the event of a liquidation,
                      ----------------------
dissolution, or winding up of the Corporation, whether voluntary or involuntary,
the holders of Series E Junior Preferred Stock shall be entitled to receive out
of the assets of the Corporation, whether such assets constitute stated capital
or surplus of any nature, an amount per share of Series E Junior Preferred Stock
equal to the Liquidation Preference, which is $5.00 for the entire 900,000
shares to be prorated to the number of Series E Junior Preferred Stock then
outstanding and no more, before any payment shall be made or any assets
distributed to the holders of Junior Liquidation Stock; provided, however, that
such rights shall accrue to the holders of Series E Junior  Preferred Stock only
in the event that the Corporation's payments with respect to the liquidation
preference of the holders of Senior Liquidation Stock are fully met.  After the
liquidation preferences of the Senior Liquidation Stock are fully met, the
entire assets of the Corporation available for distribution shall be distributed
ratably among the holders of the Series E Junior Preferred Stock and any Parity
Liquidation Stock in proportion to the respective preferential amounts to which
each is entitled (but only to the extent of such preferential amounts).  After
payment in full of the Liquidation Preference of the shares of Series E Junior
Preferred Stock and the liquidation preference of the shares of Parity
Liquidation Stock, the holders of such shares shall not be entitled to any
further participation in any distribution of assets by the Corporation.  Neither
a consolidation or merger of the Corporation with another corporation nor a sale
or transfer of all or part of the Corporation's assets for cash, securities, or
other property in and of itself will be considered a liquidation, dissolution or
winding up of the Corporation.

          Section 6.  No Mandatory Redemption.  The shares of Series E Junior
                      -----------------------
Preferred Stock shall not be subject to mandatory redemption by the Corporation.

          Section 7.  No Sinking Fund.  The shares of Series E Junior Preferred
                      ---------------
Stock shall not be subject to the operation of a purchase, retirement or sinking
fund.

                                       2
<PAGE>

          Section 8.  Optional Redemption.
                      -------------------

          (a)  Corporation Optional Redemption.  If the Corporation shall be in
               -------------------------------
compliance in all material respects with its obligations to the holders of
shares of Series E Junior Preferred Stock, , then the Corporation shall have the
right, exercisable by giving a Corporation Optional Redemption Notice not less
than 30 days or more than 60 days prior to the Redemption Date to all holders of
record of the shares of Series E Junior  Preferred Stock, at any time to redeem
all or from time to time to redeem any part of the outstanding shares of Series
E Junior Preferred Stock in accordance with this Section.  If the Corporation
shall redeem less than all outstanding shares of Series E Junior Preferred
Stock, such redemption shall be made as nearly as practical pro rata from all
holders of shares of Series E Junior Preferred Stock.  Any Corporation Optional
Redemption Notice under this Section shall be given to the holders of record of
the shares of Series E Junior Preferred Stock at their addresses appearing on
the records of the Corporation; provided, however, that any failure or defect in
the giving of such notice to any such holder shall not affect the validity of
notice to or the redemption of shares of Series E Junior Preferred Stock of any
other holder.  On the Redemption Date (or such later date as a holder of shares
of Series E Junior Preferred Stock surrenders to the Corporation the
certificate(s) for shares of Series E Junior Preferred Stock to be redeemed
pursuant to this Section the Corporation shall make payment of the applicable
Redemption Price to each holder of shares of Series E Junior Preferred Stock.
The Redemption Price for each outstanding share of Series E Junior Preferred
Stock will be one (1) share of unregistered $.01 par value common stock of the
Corporation.  Each holder of Series E Junior Preferred Stock acknowledges that
any common stock received may not have been registered under the Securities Act
of 1933;  will be acquired for their own account without any view to the further
distribution thereof; that they can afford the economic risk of holding such
securities for an indefinite period  and can afford to suffer a complete
economic loss of my investments in these Securities; that they understand and
take cognizance of the economic risks related to said Securities; have such
knowledge and experience in financial and business matters so as to be capable
of evaluating the risk of investment in these Securities; and has been furnished
the most recent 10K filing by the Corporation and all other financial
information considered by them to be relevant to the decision to acquire the
Securities.

          (b)  Final Redemption.  The Corporation shall have the obligation to
               ----------------
redeem all, but not less than all, outstanding shares of Series E Junior
Preferred Stock on the fifth (5th) anniversary of the date of its issuance.

          at the option of the Corporation except as provided in Sections 9(a)
and 9(b).

          Section 9.  Conversion.
                      ----------

          (a)  Conversion at Option of Holder.  The holders of the Series E
               ------------------------------
Junior Preferred Stock  shall have no rights to convert the preferred stock to
common

                                       3
<PAGE>

stock. The Corporation shall have no obligation to reserve any common stock in
connection with the issuance of Series E Junior Preferred Stock.

          Section 10.  Voting Rights; Certain Restrictions.
                       -----------------------------------

          (a)  Voting Rights.  Except as otherwise required by law or expressly
               --------------
provided herein, shares of Series E Junior Preferred Stock shall not be entitled
to vote on any matter.

          (b)  Articles of Incorporation; Certain Stock.  The affirmative vote
               ----------------------------------------
or consent of the holders of a majority of the outstanding shares of the Series
E Junior Preferred Stock, voting separately as a class, will be required for (1)
any amendment, alteration, or repeal, whether by merger or consolidation or
otherwise, of the Corporation's Articles of Incorporation if the amendment,
alteration, or repeal materially and adversely affects the powers, preferences,
or special rights of the Series D Convertible Preferred Stock, or (2) the
creation and issuance of any Senior Dividend Stock or Senior Liquidation Stock;
provided, however, that any increase in the authorized Preferred Stock of the
Corporation or the creation and issuance of any stock which is both Junior
Dividend Stock and Junior Liquidation Stock shall not be deemed to affect
materially and adversely such powers, preferences, or special rights and any
such increase or creation and issuance may be made without any such vote by the
holders of Series D Convertible Preferred Stock except as otherwise required by
law.

          (c)  Repurchases of Series E Junior Preferred Stock.  The Corporation
               ----------------------------------------------
shall not repurchase or otherwise acquire any shares of Series E Junior
Preferred Stock unless the Corporation offers to repurchase or otherwise acquire
simultaneously a pro rata portion of each holder's shares of Series E Junior
Preferred Stock for cash at the same price per share.

          (d)  Other.  So long as any shares of Series E Junior Preferred Stock
               -----
are outstanding:

          (1)  Payment of Obligations.  The Corporation will pay and discharge,
               ----------------------
and will cause each subsidiary of the Corporation to pay and discharge, when due
all their respective obligations and liabilities which are material to the
Corporation and its subsidiaries taken as a whole, including, without
limitation, tax liabilities, except where the same may be contested in good
faith by appropriate proceedings.

          (2)  Maintenance of Property; Insurance.  (A)  The Corporation will
               ----------------------------------
keep, and will cause each subsidiary of the Corporation to keep, all material
property useful and necessary in its business in good working order and
condition, ordinary wear and tear excepted.

          (B)  The Corporation will maintain, and will cause each subsidiary of
the Corporation to maintain, with financially sound and responsible insurance
companies, insurance against loss or damage by fire or other casualty and such
other insurance,

                                       4
<PAGE>

including but not limited to, product liability insurance, in such amounts and
covering such risks as is reasonably adequate for the conduct of their
businesses and the value of their properties.

          (3)  Conduct of Business and Maintenance of Existence.  The
               ------------------------------------------------
Corporation will continue, and will cause each subsidiary of the Corporation to
continue, to engage in business of the same general type as conducted by the
Corporation and its operating subsidiaries at the time this Statement of
Resolution filed with the Secretary of State of the State of Texas, and will
preserve, renew and keep in full force and effect, and will cause each
subsidiary of the Corporation to preserve, renew and keep in full force and
effect, their respective corporate existence and their respective material
rights, privileges and franchises necessary or desirable in the normal conduct
of business.

          (4)  Compliance with Laws.  The Corporation will comply, and will
               --------------------
cause each subsidiary of the Corporation to comply, in all material respects
with all applicable laws, ordinances, rules, regulations, decisions, orders and
requirements of governmental authorities and courts (including, without
limitation, environmental laws) except (i) where compliance therewith is
contested in good faith by appropriate proceedings or (ii) where non-compliance
therewith could not reasonably be expected to have a material adverse effect on
the business, condition (financial or otherwise), operations, performance,
properties or prospects of the Corporation and its subsidiaries, taken as a
whole.

          (5)  Investment Company Act.  The Corporation will not be or become an
               ----------------------
open-end investment trust, unit investment trust or face-amount certificate
company that is or is required to be registered under Section 8 of the
Investment Company Act of 1940, as amended, or any successor provision.

          (6)  Transactions with Affiliates.  The Corporation will not, and will
               ----------------------------
not permit any subsidiary of the Corporation, directly or indirectly, to pay any
funds to or for the account of, make any investment (whether by acquisition of
stock or indebtedness, by loan, advance, transfer of property, guarantee or
other agreement to pay, purchase or service, directly or indirectly, any
indebtedness, or otherwise) in, lease, sell, transfer or otherwise dispose of
any assets, tangible or intangible, to, or participate in, or effect any
transaction in connection with, any joint enterprise or other joint arrangement
with, any Affiliate of the Corporation, except, on terms to the Corporation or
such subsidiary no less favorable than terms that could be obtained by the
Corporation or such subsidiary from a person that is not an Affiliate of the
Corporation, as determined in good faith by the Board of Directors.

          (7)  Compliance.  The Corporation shall (a) use its commercially
               -----------
reasonable best efforts to obtain knowledge of any failure or default by the
Corporation in the timely performance of any material obligation to the holders
of the Series D Convertible Preferred Stock under the terms of this Statement of
Resolution, the Exchange Agreements, the Registration Rights Agreement, the
Transfer Agent

                                       5
<PAGE>

Instruction or any other document or instrument executed and delivered by the
Corporation in connection herewith or therewith and (b) shall notify the holders
of the Series D Convertible Preferred Stock promptly, but in no event later than
three Business Days after the Corporation first learns of any such failure or
default.

          Section 11.  Miscellaneous.
                       -------------

          (a)  Notices.  Any notices required or permitted to be given under the
               -------
terms of this Statement of Resolution shall be in writing and shall be sent by
mail or delivered personally (which shall include telephone line facsimile
transmission) or by courier and shall be deemed given five days after being
placed in the mail, if mailed, or upon receipt, if delivered personally or by
courier (a) in the case of the Corporation, addressed to the Corporation at 1250
Wood Branch Park Drive, Houston, Texas, 77079, Attention:  Chief Executive
Officer (telephone line facsimile transmission number (281) 529-4650), or, in
the case of any holder of shares of Series D Convertible Preferred Stock, at
such holder's address or telephone line facsimile transmission number shown on
the stock books maintained by the Corporation with respect to the Series D
Convertible Preferred Stock or such other address as the Corporation shall have
provided by notice to the holders of shares of Series D Convertible Preferred
Stock in accordance with this Section or any holder of shares of Series D
Convertible Preferred Stock shall have provided to the Corporation in accordance
with this Section.

          (b)  Replacement of Certificates.  Upon receipt by the Corporation of
               ---------------------------
evidence reasonably satisfactory to the Corporation of the ownership of and the
loss, theft, destruction or mutilation of any certificate for shares of Series D
Convertible Preferred Stock and (1) in the case of loss, theft or destruction,
of indemnity from the record holder of the certificate for such shares of Series
D Convertible Preferred Stock reasonably satisfactory in form to the Corporation
(and without the requirement to post any bond or other security) or (2) in the
case of mutilation, upon surrender and cancellation of the certificate for such
shares of Series D Convertible Preferred Stock, the Corporation will execute and
deliver to such holder a new certificate for such shares of Series D Convertible
Preferred Stock without charge to such holder.

          (c)  Overdue Amounts.  Except as otherwise specifically provided in
               ---------------
Section 5 with respect to dividends in arrears on the Series D Convertible
Preferred Stock, whenever any amount which is due to any holder of shares of
Series D Convertible Preferred Stock is not paid to such holder when due, such
amount shall bear interest at the rate of 14% per annum ( or such other rate as
shall be the maximum rate allowable by applicable law) until paid in full.

                                       6
<PAGE>

          IN WITNESS WHEREOF, Equalnet Communications Corp. has caused this
certificate to be signed by Mitchell H. Bodian, its Chief Executive Officer, as
of the 15th day of June, 1999.
       ----        ----

                                      EQUALNET COMMUNICATIONS CORP.



                                      By: /s/ Mitchell H. Bodian
                                          ---------------------------
                                          Mitchell H. Bodian

                                       7