Exhibit 31.1

CERTIFICATION

I, Kenneth A. Shewer, do hereby certify that:



| | 1. | I have reviewed this Report on Form 10-K of World Monitor Trust III - Series J (Registrant);
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| | 2. | Based on my knowledge, this Report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with respect to the period covered by this Report;
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| | 3. | Based on my knowledge, the financial statements, and other financial information included in this Report, fairly present in all material respects the financial condition, results of
operations and cash flows of Registrant as of, and for, the periods presented in this Report;
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| | 4. | Registrants other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as such term is defined in Exchange Act Rules
13a-15(e) and 15d-15(e)) and internal control over financial reporting) as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for Registrant and we have:
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| | a) | Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information
relating to Registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this Report is being prepared;
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| | b) | Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable
assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;
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| | c) | Evaluated the effectiveness of Registrants disclosure controls and procedures and presented in this Report our conclusions about the effectiveness of the disclosure controls
and procedures, as of the end of the period covered by this Report based on such evaluation; and
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| | d) | Disclosed in this Report any change in Registrants internal control over financial reporting that occurred during Registrants most recent fiscal quarter that has
materially affected, or is reasonably likely to materially affect, Registrants internal control over financial reporting; and
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| | 5. | Registrants other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to Registrants auditors and
the audit committee of Registrants board of directors (or persons performing the equivalent functions):
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| | a) | All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect
Registrants ability to record, process, summarize and report financial information; and
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| | b) | Any fraud, whether or not material, that involves management or other employees who have a significant role in Registrants internal control over financial reporting.
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|                       |  |  |  |     |  |                              
|---------------------- |  |  |  | --- |  | -----------------------------
|Date: February 2, 2009 |  |  |  | By: |  | /s/    Kenneth A. Shewer     
|                       |  |  |  |     |  | Kenneth A. Shewer            
|                       |  |  |  |     |  | (Principal Executive Officer)