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 2, 2012

VIA EDGAR TRANSMISSION

Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

Re:	Hatteras Core Alternatives TEI Institutional Fund, L.P.
	(File Nos. 333-176625/ 811-21985)

Ladies and Gentlemen:

Filed herewith electronically via EDGAR is an amendment to the registration statement on Form N-2 (the “Registration Statement”) of Hatteras Core Alternatives TEI Institutional Fund, L.P. (the “Registrant”). The Registration Statement is being filed pursuant to the Investment Company Act of 1940, as amended, and the Securities Act of 1933, as amended (the “Securities Act”), and the applicable rules thereunder. The purpose of this amendment is to include the most current financial statements of the Registrant and to make other non-material changes. The Registrant represents that this amendment would be filed pursuant to Rule 485(b) of the Securities Act if the Registrant was an open-end management investment company.

Questions and comments may be directed to the undersigned at (215) 988-2996.

Very truly yours,

/s/ Katherine A. Corey

Katherine A. Corey

cc: Joshua B. Deringer