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**EXHIBIT 31.1**

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**Certificationof Chief Executive Officer Under**

**Section302 of the Sarbanes-Oxley Act of 2002**

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**                I, David L. Bradshaw, ChiefExecutive Officer of Tipperary Corporation certify that:**

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**                1.             I have reviewed this Quarterly Report on Form 10-Q of TipperaryCorporation (“registrant”);**

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**                2.             Based on my knowledge, this report does not contain anyuntrue statement of a material fact or omit to state a material fact necessaryto make the statements made, in light of the circumstances under which suchstatements were made, not misleading with respect to the period covered by thisreport;**

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**                3.             Based on my knowledge, the financial statements, andother financial information included in this report, fairly present in allmaterial respects the financial condition, results of operations and cash flowsof the registrant as of, and for, the periods presented in this report;**

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**                4.             The registrant’s other certifying officer and I areresponsible for establishing and maintaining disclosure controls and procedures(as defined in Exchange Act Rule 13a-15(e) and 15d-15(e)) for the registrantand have:**

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**                                               **                (a)           Designed such disclosure controls and procedures, orcaused such disclosure controls and procedures to be designed under oursupervision, to ensure that material information relating to the registrant,including its consolidated subsidiaries, is made known to us by others withinthose entities, particularly during the period in which this report is beingprepared;

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**                             **                      (b)           Reserved;

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**                                               **                (c)           Evaluated the effectiveness of the registrant’s disclosurecontrols and procedures and presented in this report our conclusions about theeffectiveness of the disclosure controls and procedures, as of the end of theperiod covered by this report based on such evaluation; and

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**                                               **                (d)           Disclosed in this report any change in the registrant’sinternal control over financial reporting that occurred during the registrant’smost recent fiscal quarter (the registrant’s fourth fiscal quarter in the caseof an annual report) that has materially affected, or is reasonably likely tomaterially affect, the registrant’s internal control over financial reporting;and

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**                5.             The registrant’s other certifying officer and I havedisclosed, based on our most recent evaluation of internal control overfinancial reporting, to the registrant’s auditors and the audit committee ofthe registrant’s board of directors (or persons performing the equivalentfunctions):**

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**                                               **                (a)           All significant deficiencies and material weaknesses inthe design of operation of internal control over financial reporting which arereasonably likely to adversely effect the registrant’s ability to record,process, summarize and report financial information; and

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**                                               **                (b)           Any fraud, whether or not material, that involvesmanagement or other employees who have a significant role in the registrant’sinternal control over financial reporting.

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| **Date:**      | **May 16,  2005**           | ** ** |
|----------------|-----------------------------|------------|
| ** **     | ** **                  | ** ** |
| **Signature:** | **/s/ David  L. Bradshaw**  | ** ** |
| ** **     | ** **                  | ** ** |
| ** **     | **David L.  Bradshaw**      | ** ** |
| **Title:**     | **Chief Executive Officer** | ** ** |

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