<PAGE>
 
                                                                    EXHIBIT 10.1

                       SHAREHOLDERS' EXCHANGE AGREEMENT

                            SOCO INTERNATIONAL PLC
                   (Registered in England under No. 3300821)


Territorial Resources



6 May 1997

Dear Sirs:

We are writing this letter further to Ed Story's letters to you of 21 January
1997 and 14 February 1997 relating to the acquisition by us of interests in the
various SOCO companies and the subsequent listing on the London Stock Exchange
of this company.  This letter deals with the agreement to acquire the various
interests in the SOCO companies as a first step to achieving that listing.  It
does not attempt to deal with the listing itself which will be the subject of
further agreements which, amongst other things, will involve the issue of new
shares for cash by SOCO International PLC ("SOCO International") and the
consequential dilution of your shareholdings.

Subject only to the satisfaction of the Conditions (as defined below) you hereby
agree to transfer to us 72 shares (the "Shares") in SOCO Tamtsag Mongolia, Inc.
("SOTAMO") in consideration for the allotment by us of such number of ordinary
shares (credited as fully paid) as shall be equal to 3.492% of the issued share
capital of SOCO International.  This percentage is calculated  after the
allotment of shares as consideration for the acquisition of interests in SOTAMO
(via certain holding companies or otherwise), SOCO Perm Russia, Inc., SOCO
Thailand, Inc., Cairn Energy Onshore Limited, Command Petroleum (Tunisia) Pty
Limited and Command Petroleum (Overseas) Limited, but before the issue of shares
for cash as part of the listing process.

The obligations set out in this letter are conditional upon:

(a)  the admission to listing on the London Stock Exchange of all the issued
     share capital of SOCO International by not later than 9:00 am on 2 June
     1997;
 
(b)  waiver of any pre-emption rights over shares in SOTAMO by those in whom
     such rights are vested;
 
(c)  the receipt by us of any necessary approvals or consents to the transfer of
     the Shares; and
 
<PAGE>
 
(d)  completion in escrow of the acquisition by us of all the issued share
     capital of Cairn Energy Onshore Limited;

     (collectively called "the Conditions").

Completion of the transfer of the Shares will take place on such date as we may
specify.  We will be permitted to specify that completion may take place in
escrow, the escrow being released on satisfaction of the Conditions (or in the
case of (b), (c) and (d), the Conditions having been waived by us).  At
completion you will take all necessary steps to transfer the Shares to us
including but not limited to the execution of all necessary documents (in
particular such documents as are required to give effect to this letter).

You agree that forthwith upon completion having taken place and the Conditions
having been satisfied (or in the case of (b), (c) and (d), having been waived by
us), the agreement governing your rights and obligations in respect of SOTAMO
("the Agreement") will be cancelled so far as you are concerned in respect of
the Shares and will be of no further force and effect in that respect save in
respect of any prior breach of the Agreement.  However, in respect of any shares
in SOTAMO which are not transferred by you or by other investors in SOTAMO, the
Agreement will continue in full force and effect.

In accepting this offer you agree with and confirm to us that:

(i)  you are not in breach of any of the terms of the Agreement and you hereby
     waive any breaches by all of the other parties to the Agreement and any
     rights of pre-emption that you may have in relation to the exchange of
     shares by such parties on similar terms to this letter;

(ii)  you have, and will continue to have until transfer of the Shares under
      this letter, absolute title to the Shares which are free of any charges,
      mortgages, liens or any other encumbrances of any nature whatsoever;

(iii) you have no claims against SOTAMO or any of its assets. In particular, but
      without limitation, if you have made any loans or advances to SOTAMO, you
      hereby attribute and assign to SOTAMO, subject only to satisfaction of the
      Conditions, all amounts owing (whether of principal or interest) by virtue
      of such loans or advances;

(iv)  you have no knowledge of any matters in relation to SOTAMO which would
      have a material adverse effect on its value;

(v)   you have not entered into any commitments in any way on behalf of or in
      relation to SOTAMO or its assets other than commitments to be discharged
      solely by you or solely for your account; and

                                       2
<PAGE>
 
(vi)  there are no restrictions imposed on you which affect your ability to
      enter this letter including without limitation any applicable securities
      laws (other than the securities laws of England) and you have made all
      necessary notifications and filings in relation hereto.

As the listing is taking place in England, this agreement and all negotiations
preceding it will be construed in accordance with the provisions of English law
and you hereby submit to the exclusive jurisdiction of the Supreme Court of
Judicature of England in relation to any claim arising out or in connection with
this agreement and you hereby irrevocably appoint Ed Story as your agent to
accept service in connection with any such proceedings.

Please sign and return the enclosed copy of this letter to indicate your
agreement to its terms.  Such agreement will also give rise to a commitment on
your part to send us all documents of title in relation to the Shares upon
request by us but such documents will be held by our solicitors Ashurst Morris
Crisp to your order pending completion of this agreement but subject to the
terms of this agreement.

Yours Faithfully



For and on behalf of
SOCO International PLC



We hereby accept the terms of this letter



__________________________________________ 
For and on behalf of Territorial Resources

                                       3