**EXHIBIT 31.01**

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**RULE13a-14(a)/15d-14(a) CERTIFICATIONS**

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I, Paul Morton, ChiefExecutive Officer, President and Manager of Merrill Lynch AlternativeInvestments LLC, the general partner of ML Trend-Following Futures Fund, L.P.certify that:

 

1. I have reviewed thisreport on Form 10-K of ML Trend-Following Futures Fund L.P.;

 

2. Based on my knowledge,this report does not contain any untrue statement of a material fact or omit tostate a material fact necessary to make the statements made, in light of the circumstancesunder which such statements were made, not misleading with respect to theperiod covered by this report;

 

3. Based on my knowledge,the financial statements, and other financial information included in thisreport, fairly present in all material respects the financial condition,results of operations and cash flows of the registrant as of, and for, theperiods presented in this report;

 

4. The registrant’s othercertifying officer and I are responsible for establishing and maintainingdisclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined inExchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant andhave:

 

*a)  Designedsuch disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that materialinformation relating to the registrant, including its consolidatedsubsidiaries, is made known to us by others within those entities, particularlyduring 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 underour supervision, to provide reasonable assurance regarding the reliability offinancial reporting and the preparation of financial statements for externalpurposes in accordance with generally accepted accounting principles;

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*c)  Evaluatedthe effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by thisreport based on such evaluation; and*

 

*d)  Disclosedin this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of an annual report) that hasmaterially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting; and*

 

5. The registrant’s othercertifying officer and I have disclosed, based on our most recent evaluation ofinternal control over financial reporting, to the registrant’s auditors and theaudit committee of registrant’s board of directors (or persons performing theequivalent functions):

 

a)  Allsignificant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely toadversely affect the registrant’s ability to record, process, summarize andreport financial information; and

 

b)  Anyfraud, whether or not material, that involves management or other employees whohave a significant role in the registrant’s internal control over financialreporting.

 
| Date: March 31, 2009                       |            |
|-------------------------------------------------|-----------------|
|                                            |            |
| By                                              | /s/ PAUL MORTON |   |
| Paul Morton                                     |            |
| Chief Executive  Officer, President and Manager |            |
| **(Principal Executive Officer)**               | ** **      |
|                                                 |                 |  |

 

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