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                                                                  EXHIBIT 10.10


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 33,036 SHARES

                         INTELECT COMMUNICATIONS, INC.
                            (a Delaware corporation)

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

                       THIS WARRANT MAY NOT BE EXERCISED
                                AND WILL BE VOID
             AFTER 6:00 P.M. CENTRAL STANDARD TIME ON MAY 20, 2003

         This warrant (the "Warrant") certifies that, for value received,
Hambrecht & Quist LLC ("H&Q"), is entitled, at any time prior to 6:00 p.m.
Central Standard Time on May 20, 2003 (the "Expiration Time"), to purchase from
Intelect Communications, Inc., a Delaware 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.

         1. The Warrant Shares are purchasable at an exercise price of $10.292
per share (the "Warrant Price"). To exercise the Warrant, the holder hereof
shall deliver to the Company (i) a written notice in the form of the
Subscription Notice attached as an exhibit hereto, stating therein the election
of such holder to exercise the Warrant in the manner provided in the
Subscription Notice; (ii) payment in full of the Warrant Price (A) in cash or
by bank check for all Warrant Shares purchased hereunder, or (B) through a
"cashless" or "net-issue" exercise of each such Warrant ("Cashless Exercise");
the holder shall exchange each Warrant subject to a Cashless Exercise for that
number of Warrant Shares determined by multiplying the number of Warrant Shares
issuable hereunder by a fraction, the numerator of which shall be the
difference between (x) the Market Price (as hereinafter defined) and (y) the
Warrant Price for each such Warrant, and the denominator of which shall be the
Market Price; the Subscription Notice shall set forth the calculation upon
which the Cashless Exercise is based, or (C) a combination of (A) and (B)
above; and (iii) delivery of this Warrant.

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         "Market Price" for any day, when used with reference to Common Stock,
shall mean the price of said Common Stock determined as follows: (x) the volume
weighted per share average price as reported by Bloomberg L.P. for the Common
Stock on such day on the principal securities exchange on which the Common
Stock is listed or admitted to trading or if no such sale takes place on such
date, the average of the closing bid and asked prices thereof as officially
reported, or, if not so listed or admitted to trading on any securities
exchange, for the Common Stock on the National Association of Securities
Dealers National Market on such date, or, if there shall have been no trading
on such date or if the Common Stock shall not be listed on such system, the
average of the closing bid and asked prices in the over-the-counter market as
furnished by any NASD member firm selected from time to time by the Company for
such purpose, in each such case, unless otherwise provided herein, averaged
over a period of ten (10) consecutive trading days prior to the date as of
which the determination is to be made; or (y) if the Common Stock shall not be
listed or admitted to trading as provided in clause (x) above, the fair market
value of the Common Stock as determined in good faith by the Board of Directors
of the Company.

         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

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         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 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.


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                  (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 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; (ii) in the opinion of counsel for the Company, concurred

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         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; or (iii) the Warrant Shares
         have already been registered under the Securities Act.

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

                           (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

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                  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 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


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<PAGE>   7

                  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 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.


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         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 follows:

         If to H&Q, to:

                  One Buch Street
                  San Francisco, CA 94104

         If to the Company, to:

                  Intelect Communications, Inc.
                  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 20th day of May, 1998.

                                                  INTELECT COMMUNICATIONS, INC.



                                                  By:
                                                     ---------------------------
                                                          Herman M. Frietsch,
                                                          Chairman of the
                                                          Board, Chief Executive
                                                          Officer



                                      -8-

<PAGE>   9


                              Subscription Notice
                                Form of Purchase

                  (to be signed only upon exercise of warrant)

TO:      INTELECT COMMUNICATIONS, INC.

         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,
Inc., 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              ,       .
                    -----        -------------  ------


                                                  ------------------------------
                                                  Signature


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