**EXHIBIT 31.01**

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**Rule 13a-14(a)/15d-14(a) Certifications**

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I, Robert M. Alderman, certify that:

 

1.  I havereviewed this report on Form 10-Q of ML Appleton FuturesAccess LLC;

 

2.  Based on myknowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, inlight of the circumstances under which such statements were made, notmisleading with respect to the period covered by this report;

 

3.  Based on myknowledge, the financial statements, and other financial information includedin this report, fairly present in all material respects the financialcondition, results of operations and cash flows of the registrant as of, andfor, the periods presented in this report;

 

4.  Theregistrant’s other certifying officer and I are responsible for establishingand maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) for the registrant and have:

 

a)  Designed such disclosure controls andprocedures, or caused such disclosure controls and procedures to be designedunder our supervision, to ensure that material information relating to theregistrant, including its consolidated subsidiaries, is made known to us byothers within those entities, particularly during the period in which thisreport is being prepared;

 

b)  Evaluated the effectiveness of the registrant’sdisclosure controls and procedures and presented in this report our conclusionsabout the effectiveness of the disclosure controls and procedures, as of theend of the period covered by this report based on such evaluation; and

 

c)  Disclosed in this report any change in theregistrant’s internal control over financial reporting that occurred during theregistrant’s most recent fiscal quarter that has materially affected, or isreasonably likely to materially affect, the registrant’s internal control overfinancial reporting; and

 

5.  Theregistrant’s other certifying officer and I have disclosed, based on our mostrecent evaluation of internal control over financial reporting, to theregistrant’s auditors and the audit committee of registrant’s board ofdirectors (or persons performing the equivalent functions):

 

a) All significantdeficiencies and material weaknesses in the design or operation of internalcontrol over financial reporting which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and reportfinancial information; and

 

b) Any fraud,whether or not material, that involves management or other employees who have asignificant role in the registrant’s internal control over financial reporting.

 

 
| Date:   May 15, 2006                 |                   |
|------------------------------------------------|------------------------|
|                                           |
| By                                             | /s/ ROBERT M. ALDERMAN |   |
| Robert M. Alderman                             |
| Chief Executive Officer, President and Manager |
| **(Principal Executive Officer)**              |
|                                                |                        |  |  |

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