CONVERTIBLE SECURITIES AGREEMENT
                   OF INTELECT COMMUNICATIONS SYSTEMS LIMITED


         THIS CONVERTIBLE  SECURITIES AGREEMENT (hereinafter the "Agreement") is
made and entered into as of this 15th day of October, 1996 by the undersigned in
connection with the sale by INTELECT  COMMUNICATIONS  SYSTEMS LIMITED, a company
organized under the laws of Bermuda (hereinafter "Seller") of certain debentures
convertible  into common  shares  (hereinafter  the  "Shares")  of Seller to (i)
INFINITY  INVESTORS LTD. a corporation  organized under the laws of Nevis,  West
Indies,  and (ii) SEACREST  CAPITAL LIMITED,  a corporation  organized under the
laws of Nevis,  West Indies  (singularly a "Buyer" and  collectively  "Buyers").
Each of the Seller  and the  Buyers  (hereinafter  collectively  the  "Parties")
hereby represent, warrant and agree as follows:

         1. AGREEMENT TO SUBSCRIBE; PURCHASE PRICE.

                  (i) Buyers hereby subscribe for $5 million principal amount of
         Series A  Convertible  Debentures  (the "Series A  Debentures")  and $5
         million  principal  amount  of  Series  B  Debentures  (the  "Series  B
         Debentures")  (collectively,  the "Debentures") convertible into Shares
         in  accordance  with the  terms  set  forth  in the form of  Debentures
         attached as Exhibits A and B to this Agreement.

                  (ii) Buyers shall pay an aggregate of Ten Million Dollars ($10
         million U.S.) (the  "Purchase  Price") for the Debentures by delivering
         same day funds in United States dollars against counter-delivery of the
         Debentures by Seller,  in each case to American  Stock Transfer & Trust
         Company (the "Transfer  Agent")  pursuant to terms of that certain Book
         Entry Transfer Agent  Agreement in the form attached  hereto as Exhibit
         C,  to  be   executed   contemporaneously   herewith   (the   "Transfer
         Agreement").

                  (iii) Infinity Investors,  Ltd. shall subscribe for $9 million
         principal  amount of the Debentures and Seacrest  Capital Limited shall
         subscribe for $1 million of the  Debentures.  Each such party shall pay
         100% of the respective principal amount thereof.

         2. BUYER'S REPRESENTATIONS AND COVENANTS.

                  Each Buyer  severally  represents,  warrants and  covenants to
         Seller as follows:


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                  (i) This Agreement has been duly authorized,  validly executed
         and  delivered  on  behalf of each  Buyer  and is a valid  and  binding
         agreement  of each  Buyer in  accordance  with its  terms,  subject  to
         general  principles  of equity and to the effect of bankruptcy or other
         similar laws affecting the enforcement of creditors' rights;

                  (ii)  Each  Buyer is  purchasing  the  Debentures  for its own
         account  for   investment   purposes   and  not  with  a  view  towards
         distribution.  Each Buyer  understands and agrees that it must bear the
         economic risks of its investment for an indefinite period of time. Each
         Buyer  has  received  and  carefully  reviewed  copies  of  the  Public
         Documents (as defined below). Each Buyer understands that the offer and
         sale of the Debentures are being made only by means of this  Agreement.
         No  representations  or  warranties  have been made to either  Buyer by
         Seller, the officers or directors of Seller, or any agent,  employee or
         affiliate  of any of them  except as set forth  herein.  Each  Buyer is
         aware that the  purchase  of the  Debentures  involves a high degree of
         risk and that it may sustain, and has the financial ability to sustain,
         the loss of its entire  investment.  Each Buyer has had the opportunity
         to ask questions of and receive  answers and  satisfactory  to it from,
         Seller's  management  regarding Seller.  Each Buyer understands that no
         Federal  or  state  governmental  authority  has made  any  finding  or
         determination  relating  to  the  fairness  of  an  investment  in  the
         Debentures  and that no Federal  or state  governmental  authority  has
         recommended or endorsed,  or will recommend or endorse,  the investment
         herein.  Each Buyer,  in making the decision to purchase the Debentures
         subscribed for, has relied upon independent  investigations  made by it
         and has not relied on any information or representations  made by third
         parties  other  than  pursuant  to  this  Agreement.   Each  Buyer  has
         significant  assets,  and  upon  consummation  of the  purchase  of the
         Debentures,  will continue to have significant  assets exclusive of the
         Debentures.  Neither  Buyer  has  been  organized  for the  purpose  of
         acquiring the Debentures;

                  (iii)  Each  Buyer  is an  "accredited  investor"  within  the
         meaning of Rule 501 of the  Securities  Act of 1933,  as  amended  (the
         "Securities Act");

                  (iv) Each  Buyer  understands  that the  Debentures  are being
         offered and sold to it in reliance  on specific  provisions  of Federal
         and state  securities  laws and that Seller is relying in part upon the
         truth and  accuracy  of the  representations,  warranties,  agreements,
         acknowledgments  and  understandings  of each Buyer set forth herein in
         order to determine the applicability of such provisions;

                  (v) Each  Buyer,  in  making  the  decision  to  purchase  the
         Debentures  subscribed for, has relied upon independent  investigations
         made by it and has not

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         relied on any  information  or  representations  made by third  parties
         other than pursuant to this Agreement; and

                  (vi) Each Buyer  understands  that neither the  Debentures nor
         the Shares have been registered  under the Securities Act and therefore
         it cannot  dispose of any or all of the Debentures or the Shares unless
         such  Debentures  or  Shares  are  subsequently  registered  under  the
         Securities Act or exemptions from such registration are available. Each
         Buyer  acknowledges  that a legend  substantially  as  follows  will be
         placed on the certificates representing the Shares:

         THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED WITHOUT A
         VIEW TO THE  DISTRIBUTION  THEREOF WITHIN THE MEANING OF THE SECURITIES
         ACT OF 1933, AS AMENDED,  AND MAY NOT BE SOLD, PLEDGED,  TRANSFERRED OR
         OTHERWISE  DISPOSED OF EXCEPT IN ACCORDANCE WITH SUCH ACT AND THE RULES
         AND  REGULATIONS  THEREUNDER AND IN ACCORDANCE  WITH  APPLICABLE  STATE
         SECURITIES  LAWS.  THE ISSUER OF THESE  SHARES WILL NOT  TRANSFER  SUCH
         SHARES EXCEPT UPON RECEIPT OF EVIDENCE SATISFACTORY TO THE COMPANY THAT
         THE REGISTRATION PROVISIONS OF SUCH ACT HAVE BEEN COMPLIED WITH OR THAT
         SUCH  REGISTRATION  IS NOT  REQUIRED  AND THAT SUCH  TRANSFER  WILL NOT
         VIOLATE ANY APPLICABLE STATE SECURITIES LAWS.

         3. SELLER'S REPRESENTATIONS AND COVENANTS.

                 Seller represents, warrants and covenants to Buyers as follows:

                  (i) Seller has been duly  incorporated and is validly existing
         and in good standing  under the laws of Bermuda.  Seller has registered
         its common shares pursuant to Section 12(G) of the Securities  Exchange
         Act of 1934, as amended (the  "Exchange  Act"),  is in full  compliance
         with all  reporting  requirements  of the  Exchange  Act,  and Seller's
         common shares traded on the Nasdaq National Market, Symbol ICOMF;

                  (ii) Seller has  furnished  each Buyer with copies of Seller's
         most recent  Annual Report on Form 10-K filed with the  Securities  and
         Exchange Commission ("SEC") and all Forms 10-Q and 8-K filed thereafter
         (the  "Public  Documents").  The Public  Documents at the time of their
         filing complied in all material  respects with the  requirements of the
         Exchange Act, and the rules and regulations thereunder,  and, as of the
         date of filing,  did not include an untrue statement of a material fact
         or omit to  state  any  material  fact  necessary  in order to make the
         statements

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         contained therein,  in light of the circumstances under which they were
         made, not misleading.  Since the date of the Public  Documents,  Seller
         has not made,  or been  required to make,  any filings  with the SEC in
         order  to  ensure  that the  Public  Documents  do not,  as of the date
         hereof, include an untrue statement of a material fact or omit to state
         any material fact necessary in order to make the  statements  contained
         therein,  in light of the  circumstances  in which they were made,  not
         misleading.  The Seller's financial  statements contained in the Public
         Documents  (i)  conform  in all  material  respects  with the rules and
         regulations of the Exchange Act, (ii) were prepared in accordance  with
         generally accepted accounting  principles,  consistently  applied,  and
         (iii) fairly state all known  liabilities  (contingent or otherwise) as
         of the date of such  financial  statements  that  were  required  to be
         reflected in such  financial  statements in accordance  with  generally
         accepted accounting principles,  consistently applied. Seller currently
         has $10,000,000 principal amount of convertible debentures outstanding,
         and  13,794,055  common  shares,  and no preferred  shares,  issued and
         outstanding;

                  (iii)  Seller  has filed all  materials  required  to be filed
         pursuant to all applicable  reporting  obligations under either Section
         13(a) or 15(d) of the Exchange  Act for a period  necessary to meet the
         eligibility  requirements  of the  SEC  with  respect  to the  use of a
         Registration  Statement  on  Form  S-3  for  the  filing  of  a  resale
         registration  statement with the SEC, and Seller  currently  meets such
         eligibility requirements;

                  (iv) The Debentures,  and the Shares when issued and delivered
         upon  conversion  thereof,  have  been  and  will be duly  and  validly
         authorized and issued,  and with respect to the Shares,  fully-paid and
         nonassessable,  free from all encumbrances and restrictions  other than
         restrictions on transfer  imposed by applicable  securities laws and/or
         this  Agreement,  and will not subject the holders  thereof to personal
         liability by reason of being such holders. Except for preemptive rights
         as to  which  Seller  has  received  effective  waivers,  there  are no
         preemptive  rights of any  shareholder  of Seller  with  respect to the
         Debentures or the Shares;

                  (v) This  Agreement  has been and,  when issued in  accordance
         with the terms hereof, the Debentures will be duly authorized,  validly
         executed  and  delivered on behalf of Seller and is a valid and binding
         agreement of Seller in accordance with its respective terms, subject to
         general  principles  of equity and to  bankruptcy or other similar laws
         affecting the enforcement of creditors' rights generally;

                  (vi) The  execution  and  delivery of this  Agreement  and the
         consummation  of the  issuance of the  Debentures,  and the Shares upon
         conversion

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         thereof, and the transactions contemplated by this Agreement do not and
         will not  conflict  with or  result in a breach by Seller of any of the
         terms or provisions of, or constitute a default under,  the articles of
         association or By-laws of Seller, or any indenture,  mortgage,  deed of
         trust or other  material  agreement or  instrument to which Seller is a
         party or by which it or any of its  properties or assets are bound,  or
         any existing applicable decree, judgment or order of any court, Federal
         or State regulatory body,  administrative  agency or other governmental
         body  having  jurisdiction  over  Seller  or any of its  properties  or
         assets;

                  (vii) No  authorization,  approval,  filing with or consent of
         any  governmental  body is required  for the  issuance  and sale of the
         Debentures,  or the Shares upon conversion  thereof, as contemplated by
         this Agreement;

                  (viii)  Except  for  a fee  which  is  payable  by  Seller  as
         contemplated  in the Transfer  Agent  Agreement  to Alpine  Capital for
         services rendered to Seller not to exceed 3% of the aggregate  purchase
         price of the Debentures,  no other person,  firm or corporation will be
         entitled to receive any brokerage  fee,  commission or similar  payment
         from Seller in connection  with the  consummation  of the  transactions
         contemplated  hereby and Seller  shall not make any such payment to any
         other person, firm or corporation;

                  (ix) Seller will comply with all  applicable  securities  laws
         and regulations with respect to the sale and issuance of the Debentures
         (and the  Shares  into  which  they  are  convertible)  to each  Buyer,
         including  but not limited to the filing of all reports  required to be
         filed in  connection  therewith  with the SEC or any stock  exchange or
         NASDAQ or any other regulatory  authority (with copies thereof provided
         to Buyer so long as any of the Debentures are  outstanding),  and shall
         maintain  its  eligibility  to use Form S-3 for the  filing of a resale
         registration statement with respect to the Shares with the SEC;

                  (x) Except as disclosed in the Public  Documents,  there is no
         action,  suit or  proceeding  before  or by any  court or  governmental
         agency  or  body,  domestic  or  foreign,  now or  pending  or,  to the
         knowledge of Seller, threatened, against or affecting Seller, or any of
         its  properties,  which could  reasonably  be expected to result in any
         material  adverse  change  in  the  business,  properties,  results  of
         operations or condition  (financial  or otherwise) of Seller,  or which
         could  reasonably  be expected to materially  and adversely  affect the
         properties or assets of Seller or which could reasonably be expected to
         interfere  with  Seller's   ability  to  consummate  the   transactions
         contemplated by this Agreement;

                  (xi) Seller is not, and is not an affiliate of, an "investment
         company"  within the meaning of the Investment  Company Act of 1940, as
         amended;

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                  (xii)  Neither  Seller nor any person acting on its behalf has
         taken or will  take any  action  (including,  without  limitation,  any
         offering of any  securities of Seller under  circumstances  which would
         require  the  integration  of such  offering  with the  offering of the
         Debentures or Shares under the Securities  Act) which might subject the
         offering  described  in this  Agreement,  the  issuance  or sale of the
         Debentures, or the Shares to the registration requirements of Section 5
         of the Securities Act;

                  (xiii)  Seller will  maintain the listing of its Shares on the
         NASDAQ Stock  Market,  and will reserve from its  authorized  shares of
         common stock a sufficient number of shares to permit conversion in full
         of all outstanding Debentures;

                  (xiv)  Until such time as Buyers  have  converted  one hundred
         percent  (100%)  of  the  Debentures  into  Shares,  Seller  shall  not
         repurchase  its common shares or otherwise  enter into any  transaction
         which would cause a decrease in the number of its common  shares issued
         and outstanding  (other than transactions  that similarly  decrease the
         number of common shares into which the Debentures are convertible);

                  (xv) Seller  agrees that it will not issue a press  release or
         other  communication  to the public  containing  either Buyer's name or
         other  identifying  information  without said Buyer's written  consent,
         except  as  required  by  law,  including  the  Exchange  Act,  and  in
         fulfilling its obligations under the Registration  Rights Agreement (as
         hereafter defined);

                  (xvi) Seller will (i) retain the  Transfer  Agent as the stock
         transfer agent of Seller and (ii) if the Transfer Agent  voluntarily or
         involuntarily  fails to so serve,  select an independent,  unaffiliated
         replacement  stock  transfer  agent  willing to  perform  the duties of
         Transfer Agent under the Transfer Agent Agreement; and

                  (xvii) This Agreement, including the Exhibits hereto, does not
         contain an untrue  statement  of  material  fact,  or,  when taken as a
         whole, omit any material fact necessary in order to make the statements
         contained herein or therein not misleading.

         4.  REGISTRATION.  Immediately  following the Closing,  Seller shall be
required, at Seller's expense, to effect the registration of the Shares issuable
upon  conversion of the Debentures  held by both Buyers under the Securities Act
and relevant Blue Sky laws.  Such  registration  shall be effected in accordance
with the terms of the Registration Rights Agreement attached hereto as Exhibit C
(the "Registration  Rights Agreement").  In the event either the registration of
the Shares  issuable upon conversion of the Debentures is not (A) effective with
the SEC within sixty (60) days of the Closing

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Date (the "Registration  Date"), or (B) such effectiveness is not maintained for
a  365  consecutive  day  period  after  the  SEC  has  declared  effective  the
registration of the Shares (such period after the SEC has declared effective the
registration of the Shares being referred to as the "Registration Period"), then
either such failure shall be a breach of the Debentures  entitling  Buyers to be
paid by Seller the "Damage Amount",  as liquidated damages and not as a penalty.
The Damage  Amount shall mean (A) $5,000 for each NASDAQ  trading day  following
the  Registration  Date in which the  registration  of the  Shares  has not been
declared effective by the SEC as provided herein, which amount shall increase to
(i) $6,666 for each  NASDAQ  trading day  commencing  thirty (30) days after the
Registration  Date and (ii) $8,333 for each NASDAQ trading day commencing  sixty
(60) days after the Registration Date, and (iii) $10,000 for each NASDAQ trading
day thereafter, in each case continuing until the registration of the Shares has
been declared effective by the SEC; and (B) without  duplication for the amounts
paid  pursuant  to (A) above,  $5,000  for each  NASDAQ  trading  day during the
Registration Period in which the effectiveness of the registration of the Shares
is not maintained with the SEC. The Damage Amount shall be payable in cash as of
the end of each calendar week  following the Delivery Date, and shall be payable
whether or not an Event of Default (as defined in the Debenture) has occurred.

         5.  CLOSING.  The  Debentures  shall be dated  and  delivered,  and the
Purchase Price shall be paid on, October 15, 1996 (the "Closing Date").

         6.  ADDITIONAL AGREEMENTS.

         Right of First  Refusal.  Seller  hereby  grants to Buyers the right of
first  refusal to purchase  all (or any part) of New  Securities  (as defined in
this  Section)  that Seller may,  from time to time,  propose to sell and issue.
"New Securities" shall mean any capital stock of Seller,  whether now authorized
or not, and rights, options or warrants to purchase said capital stock, and debt
or equity securities of any type whatsoever that are, or may become, convertible
into said capital stock; provided,  however, that the term "New Securities" does
not include securities issued in Excluded Financings. "Excluded Financings" mean
(i)  non-convertible  debt or non-convertible  preferred stock financings of any
type, (ii) underwritten public offerings of the Shares, (iii) private financings
(taking into  account all material  aspects  thereof such as  conversion  price,
issuance  price and any  warrants  issued  in  connection  therewith)  which are
consummated  at a price at least equal to the  then-current  market price of the
Shares (determined as set forth in the Debentures), (iv) project financings, (v)
bank  financings  and (vi) any capital  stock of Seller  issued  pursuant to the
warrants or other rights set forth in a disclosure  letter  previously issued by
Seller to Buyers,  (vii) the issuance,  sale, exercise or conversion or grant of
options to purchase  Shares  pursuant to any of Seller's  employee stock option,
compensation, bonus or incentive plans or otherwise, or pursuant to any existing
options and warrants disclosed in the Public Documents,  and (viii) the issuance
or sale of any

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equity or debt securities used for acquisition by Seller of operating  assets or
stock of entities to be owned and operated by Seller or a subsidiary  of Seller.
Seller  shall not,  however,  consummate  any  Excluded  Financings,  other than
pursuant to (vi), (vii) and (viii) above, on or before December 31, 1996. In the
event that Seller proposes to undertake an issuance of New Securities,  it shall
give  Buyers  written  notice  of its  intention,  describing  the  type  of New
Securities,  the price and the general terms upon which Seller proposes to issue
the same. Each Subscriber  shall have fifteen (15) days from the date of receipt
of any  such  notice  to  agree  to  purchase  all or less  than  all of the New
Securities  for the price and upon the general terms  specified in the notice by
giving  written  notice  to Seller  and  stating  therein  the  quantity  of New
Securities  to be  purchased.  If Buyers  fail to  exercise in full the right of
first refusal within such fifteen (15) day period,  then Seller shall have sixty
(60)  days  thereafter  to sell the New  Securities  with  respect  to which the
Buyers'  rights were not  exercised,  at a price and upon general  terms no more
favorable to the purchasers  thereof than specified in Seller's  notice.  In the
event that  Seller has not sold the New  Securities  within  such sixty (60) day
period,  Seller shall not thereafter  issue or sell any New  Securities  without
first offering such securities to the Buyers in the manner  provided above.  The
right of first  refusal  granted  under this Section  shall  terminate  upon the
earlier of: (i) 180 days following the Closing Date; or (ii) the date upon which
Buyers cease to own at least  one-third of the Debentures or the Shares issuable
upon conversion thereof.

         7. MISCELLANEOUS.

                  (i) This  Agreement  shall be governed by and  interpreted  in
         accordance  with  the laws of  Bermuda.  Facsimile  signatures  of this
         Agreement shall be binding on all parties hereto. All  representations,
         warranties, covenants and agreements of each party hereto shall survive
         the Closing contemplated herein.

                  (ii) This Agreement may be executed by facsimile signature and
         in counterparts,  each of which shall be deemed an original, but all of
         which together shall constitute one and the same instrument.

                  (iii) Seller shall pay to Buyers $4,000 at the Closing, in the
         manner described in the Transfer Agent  Agreement,  to reimburse Buyers
         for attorneys' fees and related costs of consummating  the transactions
         contemplated herein.



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         IT WITNESS WHEREOF,  this Agreement was duly executed on the date first
written above.

                                              Official Signatory of Buyer:

                                              INFINITY INVESTORS LTD.



                                               By:/s/ J. A. Loughran
                                               ---------------------------
                                               Title: Director
                                               ---------------------------
                                               Address:
                                               27 Wellington Road
                                               Cork, Ireland
                                               (Telephone) 011-71-355-2051
                                               (Fax) 011-71-355-4975
                                               Attn: Mr. J.A. Loughran

                                               With copy to:

                                               c/o HW Finance
                                               4000 Thanksgiving Tower
                                               1601 Elm Street
                                               Dallas, Texas 75201
                                               (Telephone) 214/720-1689
                                               (Fax) 214/721-1662
                                               Attn: Stuart J. Chassanoff, Esq.

                                               SEACREST CAPITAL LIMITED



                                               By:/s/  James E. Martin
                                                     ---------------------------
                                               Title: President
                                                     ---------------------------
                                               Address:
                                               27 Wellington Road
                                               Cork, Ireland
                                               (Telephone) 011-71-355-2051
                                               (Fax) 011-71-355-4975
                                               Attn: Mr. J.A. Loughran

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                                                 Official Signatory of Seller:

                                                 INTELECT COMMUNICATIONS SYSTEMS
                                                 LIMITED



                                                    By/s/ Peter G. Leighton
                                                    ---------------------------
                                                    Peter G. Leighton, President

                                                    Address:
                                                    Reid House, 31 Church Street
                                                    Hamilton, Bermuda
                                                    (Telephone) 441/295-8639
                                                    (Fax) 441/292-5560
                                                    Attn: Peter G. Leighton


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