EX.99.906CERT

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of the Hatteras Core Alternatives TEI Institutional Fund, L.P., does hereby certify, to such officer’s knowledge, that the report on Form N-CSR of the Hatteras Core Alternatives TEI Institutional Fund, L.P., for the period ended September 30, 2018 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable, and that the information contained in the Form N-CSR fairly presents, in all material respects, the financial condition and results of operations of the Hatteras Core Alternatives TEI Institutional Fund, L.P. for the stated period.

/s/ David B. Perkins	/s/ Candi Hughes
David B. Perkins	Candi Hughes
President, Hatteras Core Alternatives TEI	Treasurer, Hatteras Core Alternatives TEI
Institutional Fund, L.P.	Institutional Fund, L.P.

Date: 12/4/18

This statement accompanies this report on Form N-CSR pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed as filed by Hatteras Core Alternatives TEI Institutional Fund, L.P. for purposes of Section 18 of the Securities Exchange Act of 1934.