  In the minimal supersymmetric standard model (MSSM), when radiative
corrections are included, the mass of the $CP=+1$ lightest Higgs boson is
bounded by $\sim 110\ GeV$ for $m_t < 150\ GeV$ and a scale of supersymmetry
breaking $\sim\ 1\ TeV$. In non-minimal supersymmetric standard models (NMSSM)
upper bounds on the mass of the corresponding scalar Higgs boson arise if the
theory is required to remain perturbative up to scales $\gg G_F^{-1/2}$. We
have computed those bounds for two illustrative NMSSM: i) A model with an
arbitrary number of gauge singlets; ii) A model with three $SU(2)_L$ triplets
with $Y=0,\pm 1$. We have integrated numerically the corresponding
renormalization group equations (RGE), including the top and bottom quark
Yukawa couplings, and added one-loop radiative corrections. For $m_t > 91\ GeV$
the absolute bounds are $\sim 140\ GeV$ for both models.
