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EXHIBIT 31.1

CERTIFICATION OF PRINCIPAL EXECUTIVE
OFFICER

I, Keith A. Meister certify that:

1. I have reviewed this quarterly report on
Form 10-Q of American Real Estate Holdings Limited
Partnership for the period ended September 30, 2004 (the
Report);

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;

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 the
Registrant as of, and for, the periods presented in this Report;

4. The Registrants other certifying
officer and I are responsible for establishing and maintaining
disclosure controls and procedures (as defined in Exchange Act
Rules 13a-15(e) and 15d-15(e)) for the Registrant and 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 the 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;     
|
| | b) evaluated the effectiveness of the
    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                                                                                                        
|
| | c) disclosed in this Report any change in
    the Registrants internal control over financial reporting
    that occurred during the Registrants most recent fiscal
    quarter (the Registrant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 control over financial reporting.

5. The Registrants other certifying
officer and I have disclosed, based on our most recent
evaluation of internal control over financial reporting, to the
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 the 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 a significant
    role in the Registrants internal control over financial
    reporting.                                                                                                   



| |                                                      
| | -----------------------------------------------------
| | /s/ KEITH A. MEISTER                                 
| |                                                      
| | Keith A. Meister                                     
| | President and Chief Executive Officer
    of         
| | American Property Investors, Inc.,                   
| | the General Partner of                               
| | American Real Estate Holdings Limited
    Partnership

Date: December 15, 2004