**EXHIBIT 31.1****Certification Required by Rule 13a-14(a) or Rule 15d-14(a)**I, Ron E. Hooper, certify that:1. I have reviewed this quarterly report on Form 10-Q of Permian Basin Royalty Trust, for whichBank of America, N.A., acts as Trustee;2. Based on my knowledge, this quarterly report does not contain any untrue statement of a materialfact or omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this quarterly report;3. Based on my knowledge, the financial statements, and other financial information included inthis quarterly report, fairly present in all material respects the financial condition,distributable income and changes in trust corpus of the registrant as of, and for, the periodspresented in this quarterly report;4. I am responsible for establishing and maintaining disclosure controls and procedures (as definedin Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (asdefined in Exchange Act Rules 13a-15(f) and 15d-15(f)), or for causing such controls and proceduresto be established and maintained, for the registrant and I have: a) designed such disclosure controls and procedures, or caused such disclosure controlsand procedures to be designed under my supervision, to ensure that material informationrelating to the registrant, including its consolidated subsidiaries, is made known to me byothers within those entities, particularly during the period in which this quarterly reportis being prepared;  b) designed such internal control over financial reporting, or caused such internalcontrol over financial reporting to be designed under my supervision, to provide reasonableassurance regarding the reliability of financial reporting and the preparation of financialstatements for external purposes;  c) evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this quarterly report my conclusions about the effectiveness of the disclosurecontrols and procedures, as of the end of the period covered by this quarterly report basedon such evaluation;  d) disclosed in this quarterly report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of an annual report) that has materially

 
   affected, or is reasonably likely to materially affect, the registrant’s internal controlover financial reporting; and5. I have disclosed, based on my most recent evaluation of internal control over financialreporting, to the registrant’s auditors: a) all significant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely to adversely affectthe registrant’s ability to record, process, summarize and report financial information;and  b) any fraud, whether or not material, that involves management or other employees whohave a significant role in the registrant’s internal control over financial reporting.In giving the certifications in paragraphs 4 and 5 above, I have relied to the extent I considerreasonable on information provided to me by Burlington Resources Oil & Gas Company LP and RiverhillEnergy Corporation.     Date:August 5, 2005 By: /s/ RON E. HOOPER         Ron E. Hooper,    Senior Vice President and    Trust Administrator    Bank of America, N.A.