**Exhibit (31.2)**

**Certifications**
I, Paul A. Smith, certify that:
1.  I have reviewed this annual report on Form 10-K of Imperial Oil Limited; 2.  Based on my knowledge, this report does not contain any untrue statement of a material factor 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 report; 3.  Based on my knowledge, the financial statements, and other financial information included inthis report, fairly present in all material respects the financial condition, results ofoperations and cash flows of the registrant as of, and for, the periods presented in thisreport; 4.  The registrant’s other certifying officer(s) and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and have:
 a)  Designed such disclosure controlsand procedures, or caused such disclosure controls and procedures to be designed under oursupervision, to ensure that material information relating to the registrant, including itsconsolidated subsidiaries, is made known to us by others within those entities, particularlyduring the period in which this report is being prepared;  b)  Designed such internal controlover financial reporting, or caused such internal control over financial reporting to bedesigned under our supervision, to provide reasonable assurance regarding the reliability offinancial reporting and the preparation of financial statements for external purposes inaccordance with generally accepted accounting principles.  c)  Evaluated the effectiveness ofthe registrant’s disclosure controls and procedures and presented in this report ourconclusions about the effectiveness of the disclosure controls and procedures, as of the endof the period covered by this report based on such evaluation; and  d)  Disclosed in thisreport any change in the registrant’s internal control over financial reporting that occurredduring the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter inthe case of an annual report) that has materially affected, or is reasonably likely tomaterially affect, the registrant’s internal control over financial reporting; and
5.  The registrant’s other certifying officer(s) and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and theaudit committee of the registrant’s board of directors (or persons performing the equivalentfunctions):
 a)   All significant deficiencies and material weaknesses in the design or operationof internal 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 who have asignificant role in the registrant’s internal controls over financial reporting.
Date: March 9, 2005   /s/ Paul A. Smith  Paul A. Smith  Controller and Senior Vice-President,  Finance and Administration  (Principal Financial Officer)