\
CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Equity Index 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, 2004 (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
Greenwich Street Series Fund -              Greenwich Street Series Fund -
Equity Index Portfolio                      Equity Index Portfolio

/s/ R. Jay Gerken                           /s/ Andrew B. Shoup
- ---------------------------                 -------------------------------
R. Jay Gerken                               Andrew B. Shoup
Date: September 9, 2004                     Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Diversified Strategic
Income 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, 2004 (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
Greenwich Street Series Fund -            Greenwich Street Series Fund -
Diversified Strategic Income Portfolio    Diversified Strategic Income Portfolio

/s/ R. Jay Gerken                         /s/ Andrew B. Shoup
- ---------------------------               --------------------------------
R. Jay Gerken                             Andrew B. Shoup
Date: September 9, 2004                   Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Salomon Brothers
Variable Aggressive Growth Fund (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, 2004 (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
Greenwich Street Series Fund -            Greenwich Street Series Fund -
Salomon Brothers Variable Aggressive      Salomon Brothers Variable Aggressive
Growth Fund                               Growth Fund

/s/ R. Jay Gerken                         /s/ Andrew B. Shoup
- ---------------------------               --------------------------------
R. Jay Gerken                             Andrew B. Shoup
Date: September 9, 2004                   Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Salomon Brothers
Variable All Cap Value Fund (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, 2004 (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
Greenwich Street Series Fund -              Greenwich Street Series Fund -
Salomon Brothers Variable All               Salomon Brothers Variable All
Cap Value Fund                              Cap Value Fund

/s/ R. Jay Gerken                           /s/ Andrew B. Shoup
- ---------------------------                 ------------------------------
R. Jay Gerken                               Andrew B. Shoup
Date: September 9, 2004                     Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Salomon Brothers
Variable Growth & Income Fund (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, 2004 (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
Greenwich Street Series Fund -                Greenwich Street Series Fund -
Salomon Brothers Variable Growth &            Salomon Brothers Variable Growth &
Income Fund                                   Income Fund

/s/ R. Jay Gerken                             /s/ Andrew B. Shoup
- ---------------------------                   ----------------------------------
R. Jay Gerken                                 Andrew B. Shoup
Date: September 9, 2004                       Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Salomon Brothers
Variable International Equity Fund (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, 2004 (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
Greenwich Street Series Fund -              Greenwich Street Series Fund -
Salomon Brothers Variable International     Salomon Brothers Variable
Equity Fund                                 International Equity Fund

/s/ R. Jay Gerken                           /s/ Andrew B. Shoup
- ---------------------------                 -------------------------
R. Jay Gerken                               Andrew B. Shoup
Date: September 9, 2004                     Date: September 9, 2004

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 Andrew B. Shoup, Chief
Administrative Officer of Greenwich Street Series Fund - Salomon Brothers
Variable Money Market Fund (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, 2004 (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
Greenwich Street Series Fund -            Greenwich Street Series Fund -
Salomon Brothers Variable Money           Salomon Brothers Variable Money
Market Fund                               Market Fund

/s/ R. Jay Gerken                         /s/ Andrew B. Shoup
- ---------------------------               -------------------------------
R. Jay Gerken                             Andrew B. Shoup
Date: September 9, 2004                   Date: September 9, 2004

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.