  One of the main features of the Minimal Supersymmetric Standard Model (MSSM)
is the existence of an absolute tree-level upper bound $m_h$ on the mass of the
$CP=+1$ lightest Higgs boson, equal to $m_Z$, that could affect detectability
at future colliders. The above bound is spoiled by {\bf radiative corrections}
and by an {\bf enlarged Higgs sector}, as {\em e.g.} a gauge singlet. Radiative
corrections in the MSSM can push the upper bound up to $115\ GeV$ for $m_t
\simlt 150\ GeV$. The presence of an enlarged Higgs sector changes the previous
upper bound to one depending on the electroweak scale, $\tan \beta$ and the
gauge and Yukawa couplings of the theory. When radiative corrections are
included, the allowed region in the $(m_h,m_t)$ plane depends on the scale
$\Lambda$ below which the theory remains perturbative. In particular, for
models with arbitrary Higgs sectors and couplings saturating the scale
$\Lambda=10^{16}\ GeV$ we find $m_h \simlt 155\ GeV$ and $m_t \simlt 190\ GeV$.
