TIPPERARY OIL & GAS CORPORATION
                                  PLEDGE OF STOCK


December 22, 1998


     Tipperary Oil & Gas Corporation ("TOGC"), which is a wholly-owned
subsidiary of Tipperary Corporation ("Tipperary"), presently owns all of the
issued and outstanding capital stock of Tipperary Oil & Gas (Australia) Pty Ltd.
("TOGA").  In consideration of, and in order to induce Slough Estates USA Inc.
("Slough") to (a) loan funds to Tipperary as provided in a Promissory Note, of
even date herewith, in the principal amount of $5,500,000, and (b) after the
date hereof, to loan funds to TOGA, its subsidiary, as provided in a Promissory
Note in the principal amount of $6,000,000, TOGC hereby pledges all of the
presently issued and outstanding capital stock, held by TOGC (the "TOGA Stock"),
as collateral to secure repayment of the foregoing two Promissory Notes, as
provided in that certain Security Agreement, of even date herewith, between
Tipperary and Slough.  TOGC represents and warrants to Slough that it will
benefit directly or indirectly from the two loans and acknowledges that such
benefit constitutes full and sufficient consideration for this pledge.

                              TIPPERARY OIL & GAS CORPORATION


                         By:   /s/ David L. Bradshaw
                            -------------------------------------------------
                               David L. Bradshaw, President