  We study the implications of the triviality problem for the Higgs masses and
other relevant parameters in the Next to Minimal Supersymmetric Standard Model
(NMSSM). By means of triviality, a new way to constrain parameters is proposed,
and therefore we are able to derive triviality bounds on the heaviest-Higgs
mass, the lightest-Higgs mass, the soft SUSY- breaking parameters, and the
vacuum expectation value of the Higgs gauge singlet through a thorough
examination of the parameter space. The triviality upper bound on the
lightest-Higgs mass predicted by NMSSM is indeed larger than the upper bound
predicted by MSSM.
