<PAGE>   1





                                                                EXHIBIT 10.55


                                PROMISSORY NOTE
$400,000                                                            July 7, 1997


         FOR VALUE RECEIVED, the undersigned, Intelect Communications Systems
Limited, a Bermuda company ("ICSL") and Intelect Systems Corp., a Delaware
corporation ("ISC" and together with ICSL called "Maker") jointly and severally
promise to pay to Robert E. Nimon and Kim E. Nimon, jointly, together (the
"Holder"), the principal amount of FOUR HUNDRED THOUSAND DOLLARS ($400,000)
together with interest on the principal amount of this Note outstanding from
time to time, calculated from the date hereof on the basis of a 360 day year,
accruing at the rate of eight percent (8%) per annum from February 14, 1998
through maturity.  All payments by the Maker under this Note shall be in
immediately available funds.

         Payments of principal and interest hereunder shall conform to the
periodic installments specified on the amortization schedule set forth as
Attachment A hereto, which Attachment A is made a part hereof for all purposes.
All unpaid principal and accrued interest hereunder shall be paid no later than
June 1, 1998.

         This Note shall be earlier due and payable upon the occurrence at any
time of any of the following events of default (individually, "an Event of
Default" and collectively, "Events of Default"):

         (1)     default in the payment when due of any principal or interest
                 under this Note;

         (2)     the liquidation, termination of existence, dissolution,
                 insolvency or business failure of the Maker,

         (3)     Maker shall become insolvent, voluntarily or involuntarily be
                 made the subject of any proceeding provided for by any
                 bankruptcy or similar debtor relief law, be subject to the
                 appointment of any receiver or custodian, or make any
                 assignment or trust mortgage for the benefit to creditors.

         Upon the occurrence of an Event of Default referenced by subparagraph
(1) above and holder's written notice thereof to Maker, Maker shall be given
ten days from receipt of such notice to cure any such Event of Default.

         Every amount overdue under this Note shall bear interest from and
after the date on which such amount first became overdue at an annual rate
which is two (2) percentage points above the rate per year specified in the
first paragraph of this Note.  Such interest on overdue amounts under this Note
shall be payable on demand and shall accrue and be compounded monthly until the
obligation of the Maker with respect to the payment of such interest has been
discharged (whether before or after judgement).
<PAGE>   2
         In no event shall any interest charged, collected or reserved under
this Note exceed the maximum rate then permitted by applicable law and if any
such payment is paid by the Maker, then such excess sum shall be credited by
the holder as a payment of principal.

         This Note may be prepaid in part or in full at any time without
penalty.

         All payments by the Maker under this Note shall be made without
set-off or counterclaim and be free and clear and without any deduction or
withholding for any taxes or fees of any nature whatever.

         Any amounts paid under this Note shall apply first to accrued
interest, and then to principal due hereunder.

         No reference in this Note to any guaranty or other document shall
impair the obligation of the Maker, which is absolute and unconditional, to pay
all amounts under this Note strictly in accordance with the terms of this Note.

         The Maker agrees to pay on demand all costs of collection, including
reasonable attorneys' fees, incurred by the holder in enforcing the obligations
of the Maker under this Note.

         No delay or omission on the part of the holder in exercising any right
under this Note shall operate as a waiver of such right or of any other right
of such holder, nor shall any delay, omission or waiver on any one occasion be
deemed a bar to or waiver of the same or any other right on any future
occasion.

         Except as specifically provided for herein, Maker waives presentment
and demand for payment, protest, notice of protest and nonpayment, and notice
of the intention to accelerate.  Maker agrees that its liability on this Note
shall not be affected by any renewal or extension in the time of payment
hereof, by any indulgences, and hereby consents to any and all renewals,
extensions, indulgences, releases or changes, regardless of the number of such
renewals, extensions, releases, or changes.

         This Note shall be governed in all respects, including construction,
validity, terms, performance, and waiver by the laws of the State of Texas.

         All of the covenants, stipulations, promises, and agreements in this
Note contained by or on behalf of Maker shall bind its successors and assigns,
jointly and severally, whether so expressed or not.  Maker may not assign its
rights or obligations hereunder without the prior written consent of the
holder.  This Note may be transferred or assigned by the holder only upon the
prior written consent of Maker, which shall not be unreasonably withheld.

         None of the terms or provisions of this Note may be excluded, modified
or amended except by a written instrument duly executed on behalf of the holder
expressly referring to this Note and setting forth the provision so excluded,
modified or amended.
<PAGE>   3
         IN WITNESS WHEREOF, each of the corporations named as Maker hereof has
duly caused this Note to be signed on its behalf, in its corporate name and by
its duly authorized officer this 7th day of July, 1997.

                                      INTELECT COMMUNICATIONS SYSTEMS LIMITED




                                      By:    /s/ HERMAN M. FRIETSCH
                                             ---------------------------------
                                             Name:  Herman M. Frietsch
                                             Title:  Chairman and CEO



                                      INTELECT SYSTEMS CORP.



                                      By:    /s/ HERMAN M. FRIETSCH
                                             ---------------------------------
                                             Name:  Herman M. Frietsch
                                             Title:  President and CEO