<PAGE>
 
                                                                    EXHIBIT 10.3


                           NONCOMPETITION AGREEMENT



          This Noncompetition Agreement (the "Agreement") is entered into as of
July 26, 1996, by and among Teletouch Communications, Inc., a Delaware
corporation ("Teletouch"), Warren Communications, Inc., a Louisiana corporation
("Warren"), and the shareholders of Warren listed on the signature pages hereof
(individually, a "Shareholder" and collectively, the "Shareholders").

                             W I T N E S S E T H:

          WHEREAS, Teletouch and Warren are parties to that certain Asset
Purchase Agreement dated as of April 2, 1996, (the "APA") pursuant to which
Teletouch will purchase substantially all of the assets and business of Warren;
and

          WHEREAS, prior to the date hereof, the Shareholders owned all of the
issued and outstanding capital stock of Warren; and

          WHEREAS, pursuant to the APA, the execution and delivery of this
Agreement are to occur contemporaneously with the consummation of the
transactions contemplated by the APA;

          NOW, THEREFORE, in connection with the consummation of the
transactions contemplated by the APA, and for other good and valuable
consideration, the receipt and sufficiency of which are hereby mutually
acknowledged, the parties hereby agree as follows:

          1.   Agreement Not to Compete.
               ------------------------ 

               1.1.  Business of Company; Shareholders' Knowledge.  In
                     --------------------------------------------             
connection with the business of Warren, Warren has developed and perfected
business plans and procedures, marketing plans and techniques and other
procedures, methods, and processes used in connection with its business, and has
also developed a list of clients and customers with significant repeat business,
all of which are critical to the financial success of Warren in part because of
the specialized nature of the business and the locales and markets serviced by
Warren. During each Shareholder's association with Warren as an officer,
director, shareholder and/or employee, each Shareholder has become familiar with
the nature of Warren's business, its customers, and with the special techniques,
procedures and methods previously referenced.
<PAGE>
 
               1.2.  Term and Restricted Activities.
                     ------------------------------ 

                     (a)  In consideration of the foregoing and the purchase of
          the assets of Warren by Teletouch, Warren and each Shareholder hereby
          agrees that for the two (2) year period beginning on the date hereof
          (the "Term"), each Shareholder shall not, directly or indirectly, for
          his or her own account or for the account of others, as an officer,
          director, stockholder, owner, partner, employee, promoter, consultant,
          manager, advisor or otherwise, participate in the promotion,
          financing, ownership, or management of, any business which offers any
          of the same products or services presently offered by, or pursues any
          activities constituting or resembling the business of Warren within
          all Parishes of the State of Lousiana and Nueces County in the State
          of Texas (collectively, the "Restricted Area"); provided, however,
          that the Shareholders may own collectively up to five percent (5%) of
          the outstanding publicly-held securities of a publicly-held
          corporation as a passive investment so long as no Shareholder
          participates in the management or control of such corporation.

                     (b)  Warren and each Shareholder agrees during the Term not
          to solicit in any manner any business from any person or entity that
          was a customer of Warren or is now or becomes a customer of Teletouch
          or assignee or successor of Teletouch if such business involves
          providing any of the same or similar products or services in the
          Restricted Area as constituted the business of Warren. Each Share
          holder specifically acknowledges that Warren's business is regional in
          scope and is currently contained in the Restricted Area. For a period
          of four (4) years, the Shareholders agree not to solicit the full-time
          employment of the current employees of Teletouch or those employees of
          Warren who become employed by Teletouch after the purchase of the
          assets of Warren by Teletouch in accordance with the APA.

                     (c)  During the Term, Warren and each Shareholder agree not
          to file an application to operate on the 157.74 Mhz frequency in any
          parish or county in the United States in which Teletouch or its
          subsidiaries after the date hereof have operations utilizing such
          frequency.

          2.   Payments to the Shareholders.  At the Closing (as such term is
               ----------------------------                          
defined in the APA) of the transactions contemplated in the APA, and on the date
hereof, Teletouch has paid and the Shareholders have accepted as full
compensation for all covenants contained herein, the sum of $100,000 paid by
wire transfer to an account designated by Warren which funds are hereby
allocated as set forth on the signature pages hereto.
<PAGE>
 
          3.   Remedies.  In the event of a breach of Warren or a Shareholder's
               --------                                          
covenant not to compete, it is understood and agreed that Teletouch shall be
entitled to injunctive relief as well as any and all other applicable remedies
at law and in equity available to such party. Warren is, and indirectly the
Shareholders are, the recipients of consideration under the APA substantially in
excess of the consideration hereunder; Warren and the Shareholders therefore
acknowledge that any damages that Teletouch suffers due to a breach of this
Agreement shall not be limited to the consideration received hereunder. If a
court of competent jurisdiction should declare this covenant not to compete
unenforceable, in whole or in part, due to any unreasonable restriction of
duration and/or geographical area, then the parties hereto ack nowledge and
agree that such a court of law or equity shall have the express authority of the
parties to this Agreement to reform this covenant not to compete to a reasonable
restriction and/or to grant Teletouch any and all other relief, at law or in
equity, reasonably necessary to protect their respective interests. Warren and
each Shareholder expressly covenants and acknowledges that he or she considers
this restrictive covenant reasonable.

          4.   Notices.  Any notice, request, instruction, correspondence or
               -------                                    
other document to be given hereunder by either party to the other (herein
collectively called "Notice") shall be in writing and delivered in person or by
courier service requiring acknowledgment of receipt of delivery or mailed by
certified mail, postage prepaid and return receipt requested, or by telecopier,
as follows:

               If to the Shareholders or Warren, addressed to:

                     200 Flying W Drive
                     Carencro, Louisiana 70520
                     Attention: Mr. John C. Warren
 
               If to Teletouch, addressed to:

                     Teletouch Communications, Inc.
                     1000 Louisiana, Suite 600
                     Houston, Texas  77002
                     Attention:  Mr. Robert M. McMurrey

                                      -3-
<PAGE>
 
                     Telecopy:  (713) 650-3351

Notice given by personal delivery, courier service or mail shall be effective
upon actual  receipt.  Notice given by telecopier shall be confirmed by
appropriate answer back and shall be effective upon actual receipt if received
during the recipient's normal business hours, or at the beginning of the
recipient's next business day after receipt if not received during the
recipient's normal business hours.  All Notices by telecopier shall be confirmed
promptly after transmission in writing by certified mail or personal delivery.
Any party may change any address to which Notice is to be given to it by giving
Notice as provided above of such change of address.

          5.   Governing Law.  The provisions of this Agreement shall be
               -------------                                            
governed by and construed and enforced in accordance with the laws of the State
of Louisiana (excluding any conflicts-of-law rule or principle that might refer
same to the laws of another jurisdiction).

          6.   Entire Agreement; Amendments and Waivers.  This Agreement and the
               ----------------------------------------                 
APA constitute the entire agreement between the parties hereto pertaining to the
subject matter hereof and supersede all prior agreements, understandings,
negotiations and discussions, whether oral or written, of the parties, and there
are no warranties, representations or other agreements between the parties in
connection with the subject matter hereof except as set forth specifically
herein or contemplated hereby. No supplement, modification or waiver of this
Agreement shall be binding unless executed in writing by the party to be bound
thereby. The failure of a party to exercise any right or remedy shall not be
deemed or constitute a waiver of such right or remedy in the future. No waiver
of any of the provisions of this Agreement shall be deemed or shall constitute a
waiver of any other provision hereof (regardless of whether similar), nor shall
any such waiver constitute a continuing waiver unless otherwise expressly
provided.

          7.   Binding Effect and Assignment.  This Agreement shall be binding
               -----------------------------                          
upon and inure to the benefit of the parties hereto and their respective
permitted successors and assigns; but neither this Agreement nor any of the
rights, benefits or obligations hereunder shall be assigned, by operation of law
or otherwise, by any party hereto without the prior written consent of the other
party; provided, however, that it is agreed that (i) after or at the Closing, as
collateral for the financing of the transaction contemplated by this Agreement,
Teletouch may assign this Agreement and Teletouch's rights hereunder and under
other 

                                      -4-
<PAGE>
 
documents entered into in connection herewith to financial institutions or
their affiliates providing any such financing or any refinancing thereof, and
provided that, upon foreclosure or sale in lieu of foreclosure or deed in lieu
of foreclosure or deed of any of the assets of Teletouch to its affiliates of
Teletouch's rights hereunder or under other documents entered into in connection
herewith or a substantial portion thereof by or to any such financial
institutions or their affiliates, the representations, warranties, obligations,
covenants, agreements and indemnities of Warren herein and in such other
documents will inure to the benefit of such financial institutions (or their
affiliates) or any such purchaser or grantee; (ii) Warren and each Shareholder
may assign the economic benefits, but not its, his or her obligations, under
this Agreement; and (iii) Teletouch may assign its rights hereunder in whole to
any party which acquires all of the former assets and business of Teletouch or
in pertinent part to any party which acquires a portion of the former assets and
business of Teletouch in any discrete area. Nothing in this Agreement, express
or implied, is intended to confer upon any person or entity other than the
parties hereto and their respective permitted successors and assigns, any
rights, benefits or obligations hereunder.

          IN WITNESS WHEREOF, this Agreement has been executed by the parties
hereto as of the date first above written.

                                     TELETOUCH COMMUNICATIONS, INC.



                                     By:________________________________________
                                        Robert M. McMurrey
                                        Chairman and Chief Executive Officer


                                     SHAREHOLDERS:



                                     ___________________________________________
                                     John C. Warren
                                     $_____________



                                     ___________________________________________
                                     Carolyn R. Warren

                                      -5-
<PAGE>
 
                                     $_____________



                                     WARREN COMMUNICATIONS, INC.


                                     By:________________________________________
                                             John C. Warren
                                             President

                                      -6-