Drinker Biddle & Reath LLP

One Logan Square

Suite 2000

Philadelphia, PA 19103-6996

(215) 988-2700 (Phone)

(215) 988-2757 (Facsimile)

www.drinkerbiddle.com

July 27, 2018

VIA EDGAR TRANSMISSION

Securities and Exchange Commission

100 F Street, NE

Washington, DC 20549

Attn: Karen Rossotto and David Manion

Re: Hatteras Core Alternatives TEI Fund, L.P. (the “Registrant”)

File Nos. 333-220752; 811-21665

Ladies and Gentlemen:

Enclosed is a request of the Registrant and its principal underwriter for acceleration of Post Effective Amendment No. 2 to the Registrant’s Registration Statement on Form N-2 under the Securities Act of 1933, as amended, and of Amendment No. 24 to the Registrant’s Registration Statement on Form N-2 under the Investment Company Act of 1940, as amended. Please contact me at (215) 988-2497 with any questions related to this request and to notify of the effectiveness of the Registration Statement.

Sincerely,

/s/ Catherine A. DiValentino

Catherine A. DiValentino

Enclosure