Exhibit 10.6

ALTENERGY ACQUISITION CORP.

600 Lexington Avenue

9th Floor

New York, NY 10022

October 28, 2021

AltEnergy, LLC

600 Lexington Avenue

9th Floor

New York, NY 10022

Re: Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement by and among AltEnergy Acquisition Corp. (the “Company”), AltEnergy, LLC (the “Provider”), dated as of the date hereof, will confirm our agreement that, commencing on the effective date (the “Effective Date”) of the Registration Statement on Form S-1 filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) for the Company’s initial public offering and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

i. Providers shall make available, or cause to be made available, to the Company, 600 Lexington Avenue, 9^th Floor, New York, NY 10022 (or any successor location designated by Providers), certain office space, utilities and secretarial and administrative support services as may be reasonably required by the Company. In exchange therefor, the Company shall pay the Provider the sum of $15,000 per month, on the Effective Date and continuing monthly thereafter until the Termination Date; and

ii. The Provider hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This letter agreement constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

[Signature Page Follows]

Very truly yours,
ALTENERGY ACQUISITION CORP.
By:	/s/ Russell Stidolph
Name:	Russell Stidolph
Title:	Chief Executive Officer

AGREED TO AND ACCEPTED BY:
AltEnergy, LLC
By:	/s/ Russell Stidolph
Name:	Russell Stidolph
Title:	Manager

[Signature Page to Administrative Services Agreement]