CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. JAY GERKEN, Chief Executive Officer, and RICHARD PETEKA, Chief Financial
Officer of Greenwich Street Series Fund - Appreciation Portfolio (the
"Registrant"), each certify to the best of his or her knowledge that:

1. The Registrant's periodic report on Form N-CSRS for the period ended June
30, 2003 (the "Form N-CSRS") 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-CSRS fairly presents, in all material
respects, the financial condition and results of operations of the Registrant.


Chief Executive Officer                      Chief Financial Officer
Greenwich Street Series Fund -               Greenwich Street Series Fund -
Appreciation Portfolio                       Appreciation Portfolio

/s/ R. Jay Gerken                            /s/ Richard Peteka
- ---------------------------                  -----------------------------------
R. Jay Gerken                                Richard Peteka
Date: August 28, 2003                        Date: August 28, 2003

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

CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. JAY GERKEN, Chief Executive Officer, and RICHARD PETEKA, Chief Financial
Officer of Greenwich Street Series Fund - Intermediate High Grade Portfolio (the
"Registrant"), each certify to the best of his or her knowledge that:

1. The Registrant's periodic report on Form N-CSRS for the period ended June
30, 2003 (the "Form N-CSRS") 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-CSRS fairly presents, in all material
respects, the financial condition and results of operations of the Registrant.


Chief Executive Officer                      Chief Financial Officer
Greenwich Street Series Fund -               Greenwich Street Series Fund -
Intermediate High Grade Portfolio            Intermediate High Grade Portfolio

/s/ R. Jay Gerken                            /s/ Richard Peteka
- ---------------------------                  -----------------------------------
R. Jay Gerken                                Richard Peteka
Date: August 28, 2003                        Date: August 28, 2003

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

CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                 CERTIFICATION

R. JAY GERKEN, Chief Executive Officer, and RICHARD PETEKA, Chief Financial
Officer of Greenwich Street Series Fund - Fundamental Value Portfolio (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 June
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 Financial Officer
Greenwich Street Series Fund -               Greenwich Street Series Fund -
Fundamental Value Portfolio                  Fundamental Value Portfolio

/s/ R. Jay Gerken                            /s/ Richard Peteka
- ---------------------------                  -----------------------------------
R. Jay Gerken                                Richard Peteka
Date: August 28, 2003                        Date: August 28, 2003

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