SECURITY AGREEMENT


     THIS AGREEMENT is made this 22nd day of December 1998, by and between
Tipperary Corporation, a Texas corporation ("Debtor"), whose principal place of
business is 633 Seventeenth Street, Suite 1550, Denver, Colorado 80202, and
Slough Estates USA Inc., a Delaware corporation ("Secured Party"), whose office
is located at 33 West Monroe Street, Suite 2000, Chicago, Illinois 60603.

     In consideration of the mutual covenants and promises set forth herein,
Debtor and Secured Party agree:

     1.   Debtor, as to itself and on behalf of any direct or indirect
subsidiary of Debtor located in the United States (including Debtor's wholly-
owned subsidiary, Tipperary Oil & Gas Corporation, which owns all of the issued
and outstanding shares of Tipperary Oil & Gas (Australia) Pty Ltd. ("TOGA"),
hereby grants or shall cause to be granted to Secured Party a security interest
in the Collateral, as set forth in Section 2, to secure performance and payment
of certain Promissory Notes, (i) the first, of even date herewith, payable to
Secured Party by Debtor in the amount of $5,500,000 and (ii) the second, to be
made after the date hereof, payable to Secured Party by TOGA in the amount of
$6,000,000.  The $6,000,000 Promissory Note is subject to that certain Loan
Agreement, of even date herewith, between TOGA and Secured Party (the "Loan
Agreement").  Capitalized terms not otherwise defined herein shall have the
meanings set forth in the Loan Agreement.

     2.   The Collateral subject to this Agreement consists of:

          (a)  a pledge of all of the present and future issued and outstanding
stock of TOGA except for such shares as are owned by Secured Party (the
certificate for such pledged shares, together with stock power endorsed in blank
for transfer, being herewith delivered to Secured Party) to secure repayment of
the above two Promissory Notes; and

          (b)  a security interest in all material, consolidated assets of
Debtor located in the United States (excluding (1) any and all properties and
assets covered or purported to be covered by the Third Amended and Restated
Mortgage, Deed of Trust, Assignment of Proceeds, Security Agreement and
Financing Statement (Oil and Gas) dated March 30, 1992, effective as of October
4, 1990, from Debtor, et al., for the benefit of U.S. Bank National Association
f/k/a Colorado National Bank f/k/a Central Bank National Association ("Senior
Lender"), (2) any and all properties and assets covered or purported to be
covered by the Negative Pledge Agreement dated as of March 31, 1994 from Debtor,
et al., for the benefit of Senior Lender, (3) any and all other oil and/or gas
properties and related assets to which Senior Lender has given value in
determining the "Borrowing Base" pursuant to the Revolving Credit and Term Loan
Agreement dated as of March 30, 1992, as amended, between Debtor, et al. and
Senior Lender, and (4) any and all proceeds of the property and assets described
in (1) through (3) above), to secure repayment of the foregoing Promissory
Notes, subject to the following prior and otherwise permitted liens:

               (i)  purchase money liens, liens existing on property at the time
     of acquisition and liens on the property of a corporation at the time it
     becomes a subsidiary of Debtor or of a direct or indirect subsidiary of
     Debtor (provided such liens are not incurred in contemplation of such
     acquisition);

               (ii) liens for taxes, assessments or other governmental charges
     or levies not yet due or which are being contested in good faith by
     appropriate proceedings;

               (iii)     liens in connection with workmen's compensation,
     unemployment insurance or other social security, old age pension or public
     liability obligations or to secure the performance of statutory
     obligations, tenders, surety and appeal bonds, bids or contracts (other
     than the payment of indebtedness of Debtor or of any of its direct or
     indirect subsidiaries, except for such contracts as are secured by liens
     otherwise permitted hereunder) in the ordinary course of business;

               (iv) liens in connection with any litigation or other legal
     proceeding or arising out of a judgment or award with respect to which an
     appeal is being prosecuted;


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               (v)  landlord's, vendor's, carrier's, warehousemen's,
     repairmen's, mechanic's, workmen's, materialmen's, construction or similar
     liens incurred in the ordinary course of business or which are being
     contested in good faith by appropriate proceedings;

               (vi) easements, rights-of-way, restrictions and other similar
     encumbrances which, in the aggregate, do not materially adversely interfere
     with the occupation, use and enjoyment of the property encumbered thereby;

               (vii)     extensions, renewals and replacements of the foregoing,
     and other non-material liens incurred in the ordinary course of business;
     and

               (viii)    liens securing debt created under capital leases.

     3.   Upon any default hereunder, Secured Party may proceed to exercise any
and all rights and remedies provided by Colorado law.

     4.   This Agreement shall be construed according the laws of the State of
Colorado.

     5.   At such time, and subject to such conditions, as hereafter provided,
in place of the pledge of TOGA stock herein provided as security, Debtor shall
cause TOGA to substitute collateral under this Agreement (the "Collateral
Substitution") consisting of (i) TOGA's right, title and interest in Petroleum
Leases 90, 91 and 92 relating to the Project (the "Project Leases") and (ii) an
assignment to Secured Party of all security interests, granted by other
participants in the Comet Ridge Project in connection with any loans made by
TOGA to such participants under Section 5.2(c) of the Loan Agreement (the "Loan
Participants").  The Collateral Substitution shall promptly take place following
such time as the Minister for Mines and Energy of Queensland, Australia,
consents to:

          (a)  the transfer to TOGA of, and the transfer to Secured Party of a
security interest in, TOGA's proportionate right, title and interest in the
Project Leases;

          (b)  the transfer to each Loan Participant of, the transfer to TOGA of
a security interest in, and the transfer by TOGA thence to Secured Party of such
security interest in, such Loan Participant's proportionate right, title and
interest in the Project Leases.

The Collateral Substitution shall be subject to the execution of such reasonable
documentation as may be necessary for such security interests to be perfected to
the reasonable satisfaction of Secured Party.

     6.   This Agreement is subject to the terms and provisions of a
Subordination Agreement dated as of December 20, 1996, as the same may
heretofore have been, or may hereafter be, amended, between Secured Party and
Senior Lender, which terms and provisions are incorporated herein by reference.

     7.   The invalidity or unenforceability of any particular provisions of
this Agreement shall not affect the other provisions hereof, and this Agreement
shall be construed in all respects as if such invalid or unenforceable
provisions were omitted.

     IN WITNESS WHEREOF, the parties hereto have executed and delivered this
Agreement on the date first above written.

TIPPERARY CORPORATION                   SLOUGH ESTATES USA INC.



By:  /s/ David L. Bradshaw              By:  /s/ Randall W. Rohner
     --------------------------------        ---------------------------------
     David L. Bradshaw, President and        Randall W. Rohner, Vice President
     and Chief Executive Officer             and Chief Financial Officer

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