  We discuss effects of the light sparticles on decays of the lightest Higgs in
a supersymmetric model with nonuniversal gaugino masses at the high scale,
focusing on the `invisible' decays into neutralinos. These can impact
significanlty the discovery possibilities of the lightest Higgs at the LHC. We
show that due to these decays, there exist regions of the $M_2-\mu$ space where
the B.R. $(h \to \gamma \gamma)$ becomes dangerously low even after imposing
the LEP constraints on the sparticle masses, implying a possible preclusion of
its discovery in the $\gamma \gamma$ channel. We find that there exist regions
in the parameter space with acceptable relic density and where the ratio ${B.R.
(h \to \gamma \gamma)_{SUSY} \over B.R. (h \to \gamma \gamma)_{SM}}$ falls
below 0.6, implying loss of signal in the $\gamma \gamma$ channel. These
regions correspond to $\tilde \chi_1^+, \tilde \chi_2^0$ masses which should be
accessible already at the Tevatron. Further we find that considerations of
relic density put lower limit on the U(1) gaugino mass parameter $M_1$
independently of $\mu, \tan \beta$ and $m_0$.
