CONVERTIBLE SECURITIES AGREEMENT
                   OF INTELECT COMMUNICATIONS SYSTEMS LIMITED



         THIS CONVERTIBLE  SECURITIES AGREEMENT (hereinafter the "Agreement") is
made and entered  into as of this 7th day of June,  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
(hereinafter the "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)  SECREST  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 an  aggregate  of Five
         Million  Dollars  ($5 million  U.S.)  principal  amount of  Debentures,
         convertible  into Shares in accordance  with the terms set forth in the
         form of Debenture attached as Exhibit A to this Agreement.

                  (ii)     Buyers shall pay an aggregate of Five Million Dollars
         ($5  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,   pursuant  to  the
         Instruction  Letter in the form  attached  hereto as  Exhibit  B, to be
         executed contemporaneously herewith (the "Instruction Letter").

                  (iii)    Infinity  Investors,  Ltd. shall   subscribe  for  $4
         million of the Debentures and Secrest   Capital Limited shall subscribe
         for $1 million of the Debentures.

     2.           BUYER'S REPRESENTATIONS AND COVENANTS.

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

                  (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 of  bankruptcy  or other  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


CONVERTIBLE SECURITIES AGREEMENT - PAGE 1
(INTELECT COMMUNICATION SYSTEMS LIMITED)



         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.  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 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  relied on any  information  or  representations
         made by third parties; 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 TAKEN WITHOUT A
         VIEW TO THE  DISTRIBUTION  THEREOF WITHIN THE MEANING OF THE SECURITIES
         ACT OF 1993, 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



CONVERTIBLE SECURITIES AGREEMENT - PAGE 2
(INTELECT COMMUNICATION SYSTEMS LIMITED)



         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 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 its 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 do not 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 under which
         they were made, not misleading.  Seller currently has 12,885,537 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  duly  authorized,  validly
         executed  and  delivered on behalf of Seller and is a valid and binding
         agreement of Seller in  accordance  with its terms,



CONVERTIBLE SECURITIES AGREEMENT - PAGE 3
(INTELECT COMMUNICATION SYSTEMS LIMITED)

         subject to general principles of equity and to bankruptcy or other 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 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  Byelaws  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)   Seller will issue one or more  Debentures in the name
         of  each  Buyer  in  the  ratios   specified  in  Section  1  above  in
         denominations  of $100,000.  Upon conversion of the Debentures,  Seller
         will issue one or more certificates representing the Shares in the name
         of each Buyer,  with a legend  substantially  in the form  specified by
         Section 2(vi) above, and in such  denominations to be specified by each
         Buyer prior to conversion;

                  (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,  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)      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;

                  (xi)     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);

                  (xii)    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



CONVERTIBLE SECURITIES AGREEMENT - PAGE 4
(INTELECT COMMUNICATION SYSTEMS LIMITED)


         Buyer's  written  consent,  except as  required by law,  including  the
         Exchange Act, and in fulfilling its obligations  under the Registration
         Rights Agreement; and

                  (xiii)   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.  Buyers hereby notify Seller that they intend to
offer for public sale all or any portion of the Shares into which the Debentures
are convertible (the "Notice").  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
effective  with  the SEC  within  sixty  (60)  days  of the  Closing  Date  (the
"Registration  Date"),  then such  failure  shall be a breach of the  Debentures
entitling  Buyers to paid by Seller the "Damage Amount",  as liquidated  damages
and not as a penalty.  The Damage  Amount shall mean $500 for each $1 million of
Debentures for each NASDAQ trading day following the Registration  Date in which
the registration of the Shares is not effective with the SEC as provided herein,
which amount shall  increase to (i) $666 for each $1 million of  Debentures  for
each NASDAQ trading day in which such  registration is not effective  commencing
thirty (30) days after the Registration Date and (ii) $1,000 for each $1 million
of  Debentures  for each NASDAQ  trading day in which such  registration  is not
effective  commencing  sixty (60) days after the  Registration  Date. 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,  June 7, 1996,  or at such time to be mutually
agreed in accordance with the Instruction Letter (the "Closing Date").

        6.        ADDITIONAL AGREEMENTS.

                  (i)      Seller  hereby  grants  to  Buyers  a right  of first
         refusal on all private  financings offered by Seller within a period of
         120 days following the date of this Agreement,  except for underwritten
         private financings.  Such right of first refusal shall authorize Buyers
         or any  affiliates of Buyers which are accredited  investors,  at their
         option,  to participate in all or a portion of such  financing.  Seller
         shall  afford  Buyers at least 15 days notice to  exercise  said option
         following  delivery of the  written  terms of the  proposed  financing,
         during  which period  Buyers shall be entitled to obtain all  available
         information  from Seller with  respect to the  financing  and  Seller's
         current reports as filed with the SEC.



CONVERTIBLE SECURITIES AGREEMENT - PAGE 5
(INTELECT COMMUNICATION SYSTEMS LIMITED)


                  (ii)     Buyers  hereby  agree to  acquire  an  additional  $5
         million of debentures  from Seller on  substantially  the same terms as
         set  forth in this  Agreement,  with said sum to be  advanced  135 days
         after the Closing Date (the "Future Transaction").  Consummation of the
         Future Transaction shall be subject to the following conditions:

                           (a)      Execution   and  delivery  of  documentation
         substantially  similar to that set forth  in this  Agreement  (and  the
         Exhibits  attached  hereto)   by  each  of  Seller  and  Buyers,  where
         applicable;

                           (b)      There  shall  have been no material  adverse
         change in the business,  operations,  financial  condition,  properties
         or  prospects  of  Seller  from  the  Closing  Date  until  the date of
         consummation of the Future Transaction;

                           (c)      The current market price per share of common
         shares of Seller (as such phrase is used in the  Debenture)  shall not,
         on  average  over  a  10  trading  day  period  ending  on  the date of
         consummation  of the Future  Transaction (the "Testing Period")  be (I)
         less  than  $6.00,  or (II)  more than  $17.50;

                           (d)      The   average  trading  volume  of  Seller's
         shares of common shares on  NASDAQ  for the Testing Period shall not be
         less than 75,000;

                           (e)      Seller shall have at least 12,885,537 common
         shares issued and outstanding on the date of consummation of the Future
         Transaction; and

                           (f)      Seller shall have complied  in all  respects
         prior  to  the  date  of  the  Future  Transaction  with  all terms and
         conditions of this Agreement and of the Debentures,  including, without
         limitation,  timely  satisfying  the registration requirement set forth
         in   Section   4   by  the  applicable  Registration   Date  (and  such
         registration  statement  shall  have  continuously  remained  effective
         through the date of consummation of the Future Transaction).

        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.

                  (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.



CONVERTIBLE SECURITIES AGREEMENT - PAGE 6
(INTELECT COMMUNICATION SYSTEMS LIMITED)


                  (iii)    Seller shall pay to Buyers $7,500 at the Closing,  in
         the manner described in the Instruction Letter, to reimburse Buyers for
         attorneys'  fees and related  costs of  consummating  the  transactions
         contemplated herein.



                            [Signature page follows]


CONVERTIBLE SECURITIES AGREEMENT - PAGE 7
(INTELECT COMMUNICATION SYSTEMS LIMITED)



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

                          Official Signatory of Buyer:

                            INFINITY INVESTORS, LTD.

                            By:___________________________________
                            Title:________________________________

                            Address:
                            27 Wellington Road
                            Cork, Ireland
                            (Telephone) 353 21 501 109
                            (Fax) 353 21 501 255
                            Attn:  Mr. James G. O'Brien

                            SECREST CAPITAL LIMITED

                            By:___________________________________
                            Title:________________________________

                            Address:
                            27 Wellington Road
                            Cork, Ireland
                            (Telephone) 353 21 501 109
                            (Fax) 353 21 501 255
                            Attn:  Mr. James G. O'Brien

                            Official Signatory of Seller:

                            INTELECT COMMUNICATIONS SYSTEMS LIMITED

                            By:___________________________________
                                Peter G. Leighton, President

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




CONVERTIBLE SECURITIES AGREEMENT - PAGE 7
(INTELECT COMMUNICATION SYSTEMS LIMITED)



                                    EXHIBIT A

                                FORM OF DEBENTURE


                     (The attached form applies to Infinity)