CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Andrew B. Shoup, Chief
Administrative Officer of Salomon Brothers Global High Income Fund Inc. (the
"Registrant"), each certify to the best of his or her knowledge that:

     1. The Registrant's periodic report on Form N-CSR for the period ended
November 30, 2003 (the "Form N-CSR") fully complies with the requirements of
section 15(d) of the Securities Exchange Act of 1934, as amended; and

     2. The information contained in the Form N-CSR fairly presents, in all
material respects, the financial condition and results of operations of the
Registrant.

Chief Executive Officer                     Chief Administrative Officer
Salomon Brothers Global High Income         Salomon Brothers Global High Income
Fund Inc.                                   Fund Inc.



/s/ R. Jay Gerken                           /s/ Andrew B. Shoup
- ---------------------------                 -------------------------
R. Jay Gerken                               Andrew B. Shoup
Date:    January 30, 2004                   Date:  January 30, 2004

This certification is being furnished to the Securities and Exchange Commission
solely pursuant to 18 U.S.C. ss. 1350 and is not being filed as part of the Form
N-CSR with the Commission.