Hatteras Core Alternatives TEI Institutional Fund CORRESP Correspondence with SEC

Hatteras Core Alternatives TEI Institutional Fund, L.P.

6601 Six Forks Road

Suite 340

Raleigh, NC 27615

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 Institutional Fund, L.P. (the “Registrant”)
File Nos. 333-220748; 811-21985

Ladies and Gentlemen:

Pursuant to Rule 461 under the Securities Act of 1933, as amended (the “Securities Act”), we hereby request that the effective date of Post Effective Amendment No. 2 to the Registrant’s Registration Statement on Form N-2 under the Securities Act and Amendment No. 21 to the Registrant’s Registration Statement on Form N-2 under the Investment Company Act of 1940, as amended, be accelerated to July 30, 2018, or as soon thereafter as is reasonably practicable.

Should the Commission or staff, acting pursuant to delegated authority, declare the filing effective, the Registrant acknowledges that such action does not foreclose the Commission from taking any action with respect to the filing. The Registrant further acknowledges that the action of the Commission or staff, acting pursuant to delegated authority, in declaring the filing effective does not relieve the Registrant from its full responsibility for the adequacy and accuracy of the disclosure in the filing; and the Registrant may not assert this action as a defense in any proceeding initiated by the Commission or any person under the federal securities laws of the United States.

Very truly yours,

HATTERAS CORE ALTERNATIVESTEI InstitutionalFUND, L.P.

/s/ Candi Hughes

Name: Candi Hughes

Title: Treasurer

HATTERAS CAPITAL DISTRIBUTORS, LLC

/s/ R. Lance Baker

Name: R. Lance Baker

Title: Chief Financial Officer