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                                                                   EXHIBIT 10.44


THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER 
THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), AND ARE
"RESTRICTED SECURITIES" WITHIN THE MEANING OF RULE 144 PROMULGATED UNDER THE
SECURITIES ACT.  THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT
BE SOLD OR TRANSFERRED WITHOUT COMPLYING WITH RULE 144 IN THE ABSENCE OF AN
EFFECTIVE REGISTRATION OR OTHER COMPLIANCE UNDER THE SECURITIES ACT.

                                                           WARRANT TO PURCHASE
                                                           Up to 300,000 SHARES

                    INTELECT COMMUNICATIONS SYSTEMS LIMITED
                            (a Bermuda corporation)

                          WARRANT FOR THE PURCHASE OF
                     Common Stock, $.01 Par Value per Share

                       THIS WARRANT MAY NOT BE EXERCISED
                   UNTIL DECEMBER 31, 1997, AND WILL BE VOID
           AFTER 6:00 P.M. CENTRAL STANDARD TIME ON DECEMBER 31, 2002

         This warrant (the "Warrant") certifies that, for value received, AJC,
Inc., is entitled, at any time and from time to time on or after December 31,
1997 (the "Beginning Date"), and at any time prior to 6:00 p.m. Central
Standard Time on December 31, 2002 (the "Expiration Time"), to purchase from
Intelect Communications Systems Limited, a Bermuda corporation (the "Company"),
up to the number of shares shown above (the "Warrant Shares") of common stock,
par value $.01, of the Company (the "Common Stock") by surrendering this
Warrant with the purchase form attached hereto, duly executed, at the principal
office of the Company at 1100 Executive Drive, Richardson, Texas 75081,  and by
paying in full and in lawful money of the United States of America, by cash or
cashiers' check, the purchase price of the Warrant Shares as to which this
Warrant is exercised, on all the terms and conditions hereinafter set forth.
This Warrant is originally issued pursuant to that certain Advisory Services
Agreement dated effective May 1, 1997 (the "Agreement"), by and between the
Company and Renaissance Financial Services Corp.

         1.      The purchase price at which the Warrant Shares are purchasable
(the "Warrant Price") shall be as follows:

                 a.  100,000 shares at an exercise price of $3.00 per share;

                 b.  100,000 shares at an exercise price of $5.00 per share;
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                 c.  100,000 shares at an exercise price of $7.00 per share.

         2.      On the exercise of all or any portion of this Warrant in the
manner provided above, the person exercising the same shall be deemed to have
become a holder of record of Common Stock (or of the other securities or
properties to which he or it is entitled on such exercise) for all purposes,
and certificates for the securities so purchased shall be delivered to the
purchaser within a reasonable time after the Warrant shall have been exercised
as set forth above.  If this Warrant shall be exercised with respect to only a
portion of the Warrant Shares covered hereby, the holder shall be entitled to
receive a similar warrant of like tenor and date covering the number of Warrant
Shares with respect to which this Warrant shall not have been exercised.

         3.      The Company covenants and agrees that the Warrant Shares which
may be issued on the exercise of the rights represented by this Warrant will,
upon receipt of the Warrant Price, be fully paid and nonassessable, and free
from all taxes, liens, and charges with respect to the issue thereof.  The
Company further covenants and agrees that, during the period within which the
rights represented by this Warrant may be exercised, the Company will have
authorized and reserved a sufficient number of shares of Common Stock to
provide for the exercise of the rights represented by this Warrant.

         4.      The Warrant Price and number of Warrant Shares purchasable
pursuant to this Warrant may be subject to adjustment from time to time as
follows:

                 (a)      If the Company issues any stock dividends, the
         Warrant Price in effect immediately prior to the record date for such
         stock dividend shall be proportionately decreased or, at the holder's
         option, the number of Warrant Shares exercisable hereunder shall be
         proportionately increased, such adjustment to become effective
         immediately after the opening of business on the day following such
         record date.

                 (b)      If the Company shall subdivide the outstanding shares
         of Common Stock into a greater number of shares, combine the
         outstanding shares of Common Stock into a smaller number of shares, or
         issue by reclassification any of its shares, the Warrant Price and the
         number of Warrant Shares in effect immediately prior thereto shall be
         adjusted so that the holder of this Warrant shall be entitled to
         receive, after the occurrence of any of the events described, the
         number of Warrant Shares to which the holder would have been entitled
         had this Warrant been exercised immediately prior to the occurrence of
         such event.  Such adjustment shall become effective immediately after
         the opening of business on the day following the date on which such
         subdivision, combination, or reclassification, as the case may be,
         becomes effective.

                 (c)      If any capital reorganization or reclassification of
         Common Stock, or consolidation or merger of the Company with another
         corporation or the sale of all or substantially all of its assets to
         another corporation shall be effected in such a way that




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         holders of Common Stock shall be entitled to receive stock,
         securities, or assets with respect to or in exchange for Common Stock,
         then, as a condition of such reorganization, reclassification,
         consolidation, merger or sale, lawful adequate provisions shall be
         made whereby the holder of this Warrant shall thereafter have the
         right to acquire and receive on exercise hereof such shares of stock,
         securities, or assets as would have been issuable or payable (as part
         of such reorganization, reclassification, consolidation, merger or
         sale) with respect to or in exchange for such number of outstanding
         shares of Common Stock as would have been received on exercise of this
         Warrant immediately before such reorganization, reclassification,
         consolidation, merger or sale.  In any such case, appropriate
         provision shall be made with respect to the rights and interests of
         the holder of this Warrant to the end that the provisions hereof shall
         thereafter be applicable in relation to any shares of stock,
         securities, or assets thereafter deliverable on the exercise of this
         Warrant.  In the event of a merger or consolidation of the Company
         with or into another corporation or the sale of all or substantially
         all of its assets as a result of which a number of shares of common
         stock of the surviving or purchasing corporation greater or less than
         the number of shares of Common Stock outstanding immediately prior to
         such merger, consolidation, or purchase are issuable to holders of
         Common Stock, then the Warrant Price in effect immediately prior to
         such merger, consolidation, or purchase shall be adjusted in the same
         manner as though there were a subdivision or combination of the
         outstanding shares of Common Stock.  The Company will not effect any
         such consolidation, merger, or sale unless prior to the consummation
         thereof the successor corporation resulting from such consolidation or
         merger or the corporation purchasing such assets shall assume, by
         written instrument mailed or delivered to the holder hereof at its
         last address appearing on the books of the Company, the obligation to
         deliver to such holder such shares of stock, securities, or assets as,
         in accordance with the foregoing provisions, such holder may be
         entitled to acquire on exercise of this Warrant.

                 (d)      No fraction of a share shall be issued on exercise
         hereof, but, in lieu thereof, the Company, notwithstanding any other
         provision hereof, may pay therefor in cash at the fair value of any
         such fractional share at the time of exercise.

                 (e)      Neither the purchase or other acquisition by the
         Company of any shares of Common Stock nor the sale or other
         disposition by the Company of any shares of Common Stock shall affect
         any adjustment of the Warrant Price or be taken into account in
         computing any subsequent adjustment of the Warrant Price.

         5.      This Warrant shall not be transferable or assignable.

         6.      The shares issuable on exercise of this Warrant shall be
                 restricted securities





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within the meaning of Rule 144 promulgated under the Securities Act, and all
certificates for such shares shall contain a legend in substantially the
following form:

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
         "SECURITIES ACT"), AND ARE "RESTRICTED SECURITIES" WITHIN THE MEANING
         OF RULE 144 PROMULGATED UNDER THE SECURITIES ACT.  THE SECURITIES HAVE
         BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE SOLD OR TRANSFERRED
         WITHOUT COMPLYING WITH RULE 144 IN THE ABSENCE OF AN EFFECTIVE
         REGISTRATION OR OTHER COMPLIANCE UNDER THE SECURITIES ACT."

         7.      The Company agrees to register or qualify the Warrant Shares
(but not this Warrant) for sale as follows:

                 (a)      If, at any time after October 31, 1997 and during the
         period in which the rights represented by this Warrant are exercisable
         or the holder hereof owns the Warrant Shares, the Company proposes to
         file a registration statement or notification under the Securities Act
         for the primary or secondary sale of any debt or equity security, it
         will give written notice at least 30 days prior to the filing of such
         registration statement or notification to the holders of this Warrant
         and the Warrant Shares of its intention to do so.  The Company agrees
         that, after receiving written notice from the warrant holder of his
         desire to include his Warrant Shares in such proposed registration
         statement or notification, the Company shall afford the holders of
         this Warrant and the Warrant Shares the opportunity to have their
         Warrant Shares included therein.  Notwithstanding the provisions of
         this paragraph 7(a), the Company shall have the right, at any time
         after it shall have given written notice pursuant to this paragraph
         (whether or not a written request for inclusion of the Warrant Shares
         shall be made) to elect not to file any such proposed registration
         statement or notification or to withdraw the same after the filing but
         prior to the effective date thereof.  In no event shall the Company be
         obligated to include the Warrant Shares in any registration statement
         or notification under this paragraph 7(a) if:  (i) in the written
         opinion of the underwriter, the inclusion of the Warrant Shares in
         such registration statement or notification would be materially
         detrimental to the proposed offering of debt or equity securities
         pursuant to which the Company gave notice to the holders under this
         paragraph; or (ii) in the opinion of counsel for the Company,
         concurred in by counsel for the holder hereof, that the Warrant Shares
         are not considered "restricted securities" within the meaning of Rule
         144 promulgated under the Securities Act and that registration under
         the Securities Act is therefore not required.

                 (b)      In connection with the filing of a registration
         statement, notification, or post-effective amendment under this
         section, the Company covenants and agrees:





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                          (i)     to pay all expenses of such registration
                 statement, notification, or post-effective amendment,
                 including, without limitation, printing charges, legal fees
                 and disbursements of counsel for the Company, blue sky
                 expenses, accounting fees and filing fees, but not including
                 legal fees and disbursements of counsel to the holders and any
                 sales commissions on Warrant Shares offered and sold;

                          (ii)    to take all necessary action which may
                 reasonably be required in qualifying or registering the
                 Warrant Shares included in a registration statement,
                 notification or post-effective amendment for the offer and
                 sale under the securities or blue sky laws of such states as
                 requested by the holders; provided that the Company shall not
                 be obligated to execute or file any general consent to service
                 of process or to qualify as a foreign corporation to do
                 business under the laws of any such jurisdiction; and

                          (iii)   to utilize its best efforts to keep the same
                 effective for a period of not less than 90 nor more than 120
                 days.

                 (c)      Indemnification; Contribution.

                          (i)     Indemnification by the Company.  The Company
                 agrees to indemnify and hold harmless the holders from and
                 against any and all losses, claims, damages, liabilities and
                 expenses (including reasonable costs of investigation) arising
                 out of or based upon any untrue statement or alleged untrue
                 statement of a material fact contained in any such
                 registration statement or prospectus contained therein or in
                 any amendment or supplement thereto or in any preliminary
                 prospectus, or arising out of or based upon any omission or
                 alleged omission to state therein a material fact required to
                 be stated therein or necessary to make the statements therein
                 not misleading, except insofar as such losses, claims,
                 damages, liabilities or expenses arise out of, or are based
                 upon, any such untrue statement or omission or allegation
                 thereof based upon information furnished in writing to the
                 Company by the holders or on the holders' behalf expressly for
                 use therein.

                          (ii)    Indemnification by Holders.  Each holder
                 agrees to indemnify and hold harmless, severally and not
                 jointly, the Company, its directors and officers and each
                 person, if any, who controls the Company within the meaning of
                 either Section 15 of the Securities Act or Section 20 of the
                 Exchange Act to the same extent as the foregoing indemnity
                 from the Company to the holders, but only with respect to
                 information furnished in writing by a holder or on a holder's
                 behalf expressly for use in any such registration statement or
                 prospectus relating to the Warrant Shares, any amendment or
                 supplement thereto or any preliminary prospectus, and only in
                 an amount not to exceed the





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                 proceeds of any Warrant Shares  sold by any such holder
                 thereunder.  In case any action or proceeding shall be brought
                 against the Company or its directors or officers, or any such
                 controlling person, in respect of which indemnity may be
                 sought against the holders, the holders shall have the rights
                 and duties given to the Company, and the Company or its
                 directors or officers or such controlling person shall have
                 the rights and duties given to the holders, by the preceding
                 subsection hereof.

                          (iii)   Conduct of Indemnification Proceedings.  If
                 any action or proceeding (including any governmental
                 investigation) shall be brought or asserted against any person
                 entitled to indemnification under subsections (i) or (ii)
                 above (an "Indemnified Party") in respect of which indemnity
                 may be sought from any party who has agreed to provide such
                 indemnification (an "Indemnifying Party"), the Indemnifying
                 Party shall assume the defense thereof, including the
                 employment of counsel reasonably satisfactory to such
                 Indemnified Party, and shall assume the payment of all
                 expenses.  Such Indemnified Party shall have the right to
                 employ separate counsel in any such action and to participate
                 in the defense thereof, but the fees and expenses of such
                 counsel shall be at the expense of such Indemnified Party
                 unless (A) the Indemnifying Party has agreed to pay such fees
                 and expenses or (B) the named parties to any such action or
                 proceeding (including any impleaded parties) include both such
                 Indemnified Party and the Indemnifying Party, and such
                 Indemnified Party shall have been advised by counsel that
                 there is a conflict of interest on the part of counsel
                 employed by the Indemnifying Party to represent such
                 Indemnified Party (in which case, if such Indemnified Party
                 notifies the Indemnifying Party in writing that it elects to
                 employ separate counsel at the expense of the Indemnifying
                 Party, the Indemnifying Party shall not have the right to
                 assume the defense of such action or proceeding on behalf of
                 such Indemnified Party; it being understood, however, that the
                 Indemnifying Party shall not, in connection with any one such
                 action or proceeding or separate but substantially similar or
                 related actions or proceedings in the same jurisdiction
                 arising out of the same general allegations or circumstances,
                 be liable for the fees and expenses of more than one separate
                 firm of attorneys (together with appropriate local counsel) at
                 any time for all such Indemnified Parties, which firm shall be
                 designated in writing by such Indemnified Parties).  The
                 Indemnifying Party shall not be liable for any settlement of
                 any such action or proceeding effected without its written
                 consent, but if settled with its written consent, or if there
                 be a final judgment for the plaintiff in any such action or
                 proceeding, the Indemnifying Party shall indemnify and hold
                 harmless such Indemnified Parties from and against any loss or
                 liability (to the extent stated above) by reason of such
                 settlement or judgment.

                          (iv)    Contribution.  If the indemnification
                 provided for in this Section





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                 7(c) is unavailable to the Indemnified Parties in respect of
                 any losses,    claims, damages, liabilities or judgments
                 referred to herein, then each Indemnifying Party, in lieu of
                 indemnifying such Indemnified Party, shall contribute to the
                 amount paid or payable by such Indemnified Party as a result
                 of such losses, claims, damages, liabilities and judgments in
                 the following manner as between the Company on the one hand
                 and each holder on the other, in such proportion as is
                 appropriate to reflect the relative fault of the Company       
                 on the one hand and each holder on the other in connection
                 with the statements or omissions which resulted in such
                 losses, claims, damages, liabilities or judgments, as well as
                 any other relevant equitable considerations.  The relative
                 fault of the Company on the one hand and of the holder on the
                 other shall be determined by reference to, among other things,
                 whether the untrue or alleged untrue statement of a material
                 fact or the omission or alleged omission to state a material
                 fact relates to information supplied by such party, and the
                 party's relative intent, knowledge, access to information and
                 opportunity to correct or prevent such statement or omission. 
                 No person guilty of fraudulent misrepresentation (within the
                 meaning of subsection 11(f) of the Securities Act) shall be
                 entitled to contribution from any person who was not guilty of
                 such fraudulent misrepresentation.

                          (v)     Survival.  The indemnity and contribution
                 agreements contained in this 7(c) shall remain operative and
                 in full force and effect regardless of (A) any termination of
                 this Agreement, (B) any investigation made by or on behalf of
                 any Indemnified Party or by or on behalf of the Company and
                 (C) the consummation of the sale or successive resale of the
                 Warrant Shares.

         8.      As used herein, the term "Common Stock" shall mean and include
the Common Stock authorized on the date of the original issue of this Warrant,
and shall also include any capital stock of any class of the Company thereafter
authorized that shall not be limited to a fixed sum or percentage in respect of
the rights of the holders thereof to participate in dividends and in the
distribution of assets on the voluntary or involuntary liquidation,
dissolution, or winding up of the Company; provided that the Warrant Shares
purchasable pursuant to this Warrant shall include only shares of the class
designated in the Company's Charter as Common Stock on the date of the original
issue of this Warrant or, in the case of any reorganization, reclassification,
consolidation, merger, or sale of assets of the character referred to in
paragraph 4(c) hereof, the stocks, securities, or assets provided for in such
paragraph.

         9.      This agreement shall be construed under and be governed by the
laws of the State of Texas.

         10.     Any notices required or permitted hereunder shall be
sufficiently given if delivered by hand or sent by registered or certified
mail, postage prepaid, addressed as





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follows:

         If to AJC, Inc., to:

                 200 Old Country Road, Suite #400
                 Mineola, New York  11501

         If to the Company, to:

                 Intelect Communications Systems Limited
                 1100 Executive Drive, Richardson, Texas 75081
                 Attention: Herman M. Frietsch, Chairman and 
                            Chief Executive Officer

                 With copy to:
                 Philip P. Sudan, Jr.
                 Ryan & Sudan, LLP
                 909 Fannin, Suite 3900
                 Houston, Texas 77010-1010

or such other address as shall be furnished in writing by any party to the
other, and any such notice or communication shall be deemed to have been given
as of the date delivered by hand or three days after being so deposited in the
mails.

         Dated effective this 1st day of May, 1997.

                                        INTELECT COMMUNICATIONS SYSTEMS LIMITED



                                        By:    /s/ HERMAN M. FRIETSCH
                                           -------------------------------------
                                           Herman M. Frietsch,
                                           Chairman of the Board, Chief 
                                           Executive Officer




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                                Form of Purchase

                  (to be signed only upon exercise of warrant)

TO:      INTELECT COMMUNICATIONS SYSTEMS LIMITED

         The undersigned, the owner of the attached warrant, hereby irrevocable
elects to exercise the purchase rights represented by the warrant for, and to
purchase thereunder, _____ shares of common stock of Intelect Communications
Systems Limited, and herewith makes payment of $______ therefor, and requests
that the certificate(s) for such shares be delivered to _____ _________, at
____________________________________________, and if such shall not be all of
the shares purchasable hereunder, that a new warrant of like tenor for the
balance of the shares purchasable under the attached warrant be delivered to
the undersigned.

         Dated this _____ day of _____________, 199__.


                                        _______________________________________
                                        Signature



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