STOCK PURCHASE AGREEMENT


     This Stock Purchase Agreement (the "Agreement") is made and entered into as
of the 19 day of June, 1998, by and between (i) Contran Corporation, a Delaware
corporation ("Contran"), Valhi Group, Inc., a Nevada corporation ("VGI"), and
National City Lines, Inc., a Delaware corporation ("National" and together with
Contran and VGI, the "Sellers"), on the one hand, and (ii) Valhi, Inc., a
Delaware corporation (the "Purchaser") on the other hand.

                                    Recitals

     A.   Contran is the beneficial owner of 236,371 shares (the "Contran
Shares") of the common stock, $1.00 par value per share ("Tremont Common
Stock"), of Tremont Corporation, a Delaware corporation ("Tremont"), VGI is the
record and beneficial owner of 2,361,300 shares (the "VGI Shares") of Tremont
Common Stock and National is the record and beneficial owner of 350,360 shares
(the "National Shares") of Tremont Common Stock (the Contran Shares, the VGI
Shares and the National Shares (being a total of 2,948,031 shares of Tremont
Common Stock) shall collectively be referred to in this Agreement as the
"Shares").

     B.   Each of Contran, VGI and National wish to sell the Contran, VGI and
National Shares, respectively, to the Purchaser, and the Purchaser wishes to
purchase all of the Shares, on the terms and subject to the conditions of this
Agreement (the "Transaction").

                                   Agreement

     The parties agree as follows:

                                   ARTICLE I.
                                THE TRANSACTION

     Section 1.1.  Purchase and Sale of Shares.  Against payment of the purchase
price therefor as specified in Section 1.2, on the date hereof, each of Contran,
VGI and National hereby sells, transfers, assigns and delivers to the Purchaser
the Contran Shares, VGI Shares and National Shares, respectively.  Certificates
representing the VGI Shares and the National Shares are hereby delivered
accompanied by stock powers duly endorsed in blank.  Delivery of the Contran
Shares shall be in accordance with Section 1.3.

     Section 1.2.  Purchase Price and Payment.  The Purchaser hereby purchases
all of the Shares for a purchase price of $56.00 per Share, payment for which is
hereby made as follows:

          (a)  as the purchase price for the Contran Shares, a transfer of
     $13,236,776.00 in the manner specified by Contran; and

          (b)  as the purchase price for the VGI Shares, a transfer of
     $132,232,800.00 in the manner specified by VGI; and

          (c)  as the purchase price for the National Shares, a transfer of
     $19,620,160.00 in the manner specified by National.

     Section 1.3.  Delivery of the Contran Shares.  The Contran Deferred
Compensation Trust No. 2, a trust formed by Contran under the laws of the state
of Texas, is the record owner of the Contran Shares.  As soon as practicable,
and no later than 10 business days, following the date of this Agreement,
Contran shall cause instructions to be given for the transfer and delivery of
the Contran Shares to the Purchaser.

                                  ARTICLE II.
                 REPRESENTATIONS AND WARRANTIES OF THE SELLERS

     Each of the Sellers hereby individually represents and warrants to the
Purchaser as of the date of this Agreement as follows:

     Section 2.1.  Authority.  It is a corporation validly existing and in good
standing under the laws of the state of its incorporation. It has full corporate
power and authority, without the consent or approval of any other person, to
execute and deliver this Agreement and to consummate the Transaction. All
corporate action required to be taken by or on behalf of it to authorize the
execution, delivery and performance of this Agreement has been duly and properly
taken.

     Section 2.2.  Validity.  This Agreement is duly executed and delivered by
it and constitutes its lawful, valid and binding obligation, enforceable in
accordance with its terms. The execution and delivery of this Agreement and the
consummation of the Transaction by it are not prohibited by, do not violate or
conflict with any provision of, and do not result in a default under (a) its
charter or bylaws; (b) any material contract, agreement or other instrument to
which it is a party or by which it is bound; (c) any order, writ, injunction,
decree or judgment of any court or governmental agency applicable to it; or (d)
any law, rule or regulation applicable to it, except in each case for such
prohibitions, violations, conflicts or defaults that would not have a material
adverse consequence to the Transaction.

     Section 2.3.  Ownership of Shares.  It is the beneficial owner of its
Shares and upon consummation of the transactions contemplated by this Agreement,
the Purchaser will acquire good and marketable title to its Shares, free and
clear of any liens, encumbrances, security interests, restrictive agreements,
claims or imperfections of any nature whatsoever, other than restrictions on
transfer imposed by applicable securities laws.

     Section 2.4.  Hart-Scott-Rodino. Sellers have duly filed under the Hart-
Scott-Rodino Antitrust Improvement Act of 1976 with respect to the acquisition
by Contran and/or any of its controlled subsidiaries, including Purchaser, of in
excess of 50% of Tremont and the waiting period with respect to such filing
terminated without further action by the Federal Trade Commission on March 9,
1998.

     Section 2.5. SEC Documents. To the knowledge of the officers of the
Sellers, Tremont has filed all required reports, forms, statements and other
documents with the Securities and Exchange Commission since January 1, 1997 (the
"SEC Documents"). To the knowledge of the officers of the Sellers, as of their
respective dates, the SEC Documents complied in all material respects with the
requirements of the Securities Act of 1933 and the Securities Exchange Act of
1934 and the rules and regulations thereunder. To the knowledge of the officers
of the Sellers, the financial statements contained in the SEC Documents were
prepared in accordance with generally accepted accounting practices applied on a
consistent basis and fairly present the consolidated financial position of
Tremont as of the dates thereof and for the periods then ended. Except as
reflected in the SEC Documents, to the knowledge of the officers of the Sellers,
Tremont does not have any liabilities, individually or in the aggregate, which
would have a material adverse effect on Tremont.

     Section 2.6. Absence of Material Adverse Changes. Except as disclosed in
the SEC Documents or otherwise disclosed in widely disseminated news sources, or
as otherwise disclosed to Purchaser's investment bankers, there has not been any
material adverse change in Tremont's financial condition, business or prospects.

     Section 2.7. Information Supplied. To the knowledge of the officers of the
Sellers, none of the information provided to Purchaser, or any of Purchaser's
representatives (including its investment bankers), by Sellers, Tremont or any
of their officers or representatives or any officers or representatives of NL
Industries, Inc. or Titanium Metals Corporation contained any untrue statement
of a material fact or omitted to state any material fact required to be stated
or necessary in order to make the information, in light of the circumstances
under which the information was provided, not misleading.

                                  ARTICLE III.
                REPRESENTATIONS AND WARRANTIES OF THE PURCHASER

     The Purchaser hereby represents and warrants to each of the Sellers as of
the date of this Agreement as follows:

     Section 3.1.  Authority.  It is a corporation validly existing and in good
standing under the laws of the State of Delaware. It has full corporate power
and authority, without the consent or approval of any other person, to execute
and deliver this Agreement and to consummate the Transaction. All corporate and
other actions required to be taken by or on behalf of it to authorize the
execution, delivery and performance of this Agreement have been duly and
properly taken.

     Section 3.2.  Validity.  This Agreement is duly executed and delivered by
it and constitutes its lawful, valid and binding obligation, enforceable in
accordance with its terms. The execution and delivery of this Agreement and the
consummation of the Transaction by it are not prohibited by, do not violate or
conflict with any provision of, and do not result in a default under (a) its
charter or bylaws; (b) any material contract, agreement or other instrument to
which it is a party or by which it is bound; (c) any order, writ, injunction,
decree or judgment of any court or governmental agency applicable to it; or (d)
any law, rule or regulation applicable to it, except in each case for such
prohibitions, violations, conflicts or defaults that would not have a material
adverse consequence to the Transaction.

     Section 3.3.  Purchase for Investment.  It is purchasing the Shares sold
and delivered to it hereunder for investment solely for its own account and not
with a view to, or for resale in connection with, the distribution thereof.  It
understands that such Shares are restricted securities under the Securities Act
of 1933, as amended (the "Securities Act"), and that such Shares must be held
indefinitely unless they are registered under the Securities Act and any
applicable state securities or blue sky laws or an exemption from such
registration is available.

     Section 3.4.  Nature of Purchaser.  It has such knowledge and experience in
financial and business matters that it is capable of evaluating the merits and
risks of the purchase of the Shares.

                                  ARTICLE IV.
                               GENERAL PROVISIONS

     Section 4.1.  Additional Purchases.  Each of the Sellers agrees not to make
or cause to be made for its account, nor permit any entity controlled by it,
directly or indirectly (other than Purchaser and entities controlled (currently
or in the future) by Purchaser), to make or cause to be made for its account any
purchases of shares of Tremont Common Stock until such time as the Purchaser and
entities controlled by Purchaser holds more than 50% of the outstanding shares
of Tremont Common Stock (prompt notice of which shall be given by the Purchaser
to each of the Sellers), unless the Purchaser shall first decline to purchase
such Shares as may be offered.  If prior to such time any Seller or entity
controlled by such Seller shall be offered shares of Tremont Common Stock for
purchase, such Seller or entity controlled by such Seller shall promptly inform
the Purchaser of that opportunity so that the Purchaser may elect to purchase
for itself all or part of such additional shares of Tremont Common Stock.

     Section 4.2.  Restricted Shares.  The Purchaser hereby consents to the
placing of a legend on any stock certificates evidencing the Shares stating that
the Shares are restricted securities and to Tremont' s issuance of stop transfer
instructions in connection with the Shares.

     Section 4.3.  Access to Information.  Each of the Sellers and the Purchaser
shall provide the other party and its respective representatives access to all
information with respect to the business of Tremont possessed by such party and
reasonably requested by the other party.

     Section 4.4.  Survival.  The representations and warranties set forth in
this Agreement shall survive the execution of this Agreement and the
consummation of the transactions contemplated herein.  The covenants and other
agreements set forth in this Agreement shall terminate on the tenth anniversary
of this Agreement.

     Section 4.5.  Amendment and Waiver.  No amendment or waiver of any
provision of this Agreement shall in any event be effective unless the same
shall be in a writing referring to this Agreement and signed by the parties
hereto, and then such amendment, waiver or consent shall be effective only in
the specific instance and for the specific purpose for which given.

     Section 4.6.  Parties and Interest.  This Agreement shall bind and inure to
the benefit of the parties named herein and their respective heirs, successors
and assigns.

     Section 4.7.  Entire Transaction.  This Agreement contains the entire
understanding among the parties with respect to the transactions contemplated
hereby and supersedes all other agreements and understandings among the parties
with respect to the subject matter of this Agreement.

     Section 4.8.  Applicable Law.  This Agreement shall be governed by and
construed in accordance with the domestic laws of the State of Delaware, without
giving effect to any choice of law or conflict of law provision or rule (whether
of the State of Delaware or any other jurisdiction) that would cause the
application of the laws of any jurisdiction other than the State of Delaware.

     Section 4.9.  Severability.  If any provision of this Agreement is found to
violate any statute, regulation, rule, order or decree of any governmental
authority, court, agency or exchange, such invalidity shall not be deemed to
effect any other provision hereof or the validity of the remainder of this
Agreement and such invalid provision shall be deemed deleted to the minimum
extent necessary to cure such violation.
     Section 4.10.  Notice.  All notices, requests, demands and other
communications hereunder shall be in writing and shall be sent by registered or
certified mail, postage prepaid as follows:

     If to Contran:      Contran Corporation
                         5430 LBJ Freeway
                         Three Lincoln Centre, Suite 1700
                         Dallas, Texas 75240-2697
                         Attention:  Secretary

     If to National:     National City Lines, Inc.
                         5430 LBJ Freeway
                         Three Lincoln Centre, Suite 1700
                         Dallas, Texas 75240-2697
                         Attention:  Secretary

     If to VGI:          Valhi Group, Inc.
                         5430 LBJ Freeway
                         Three Lincoln Centre, Suite 1700
                         Dallas, Texas 75240-2697
                         Attention:  Secretary

     If to the Purchaser:     Valhi, Inc.
                         5430 LBJ Freeway
                         Three Lincoln Centre, Suite 1700
                         Dallas, Texas 75240-2697
                         Attention:  General Counsel

     Section 4.11.  Headings.  The sections and other headings contained in this
Agreement are for reference purposes only and shall not effect in any way the
meaning or interpretation of this Agreement.

     Section 4.12.  Expenses.  Except as otherwise expressly provided herein,
each party to this Agreement shall pay its own costs and expenses in connection
with the transactions contemplated hereby.

     The parties hereto have caused this Agreement to be executed by their duly
authorized officers as of the date first written above.


                                CONTRAN CORPORATION

                                By: /s/ Steven L. Watson
                                    Steven L. Watson, Vice President



                                NATIONAL CITY LINES, INC.

                                By: /s/ Steven L. Watson
                                    Steven L. Watson, Vice President



                                VALHI GROUP, INC.

                                By: /s/ Steven L. Watson
                                    Steven L. Watson, Vice President



                                VALHI, INC.

                                By: /s/ Bobby D. O'Brien
                                    Bobby D. O'Brien, Vice President