  We study the Higgs sector of the Minimal Supersymmetric Standard Model, in
the context of proton-proton collisions at LHC and SSC energies. We assume a
relatively heavy supersymmetric particle spectrum, and include recent results
on one-loop radiative corrections to Higgs-boson masses and couplings. We begin
by discussing present and future constraints from the LEP experiments. We then
compute branching ratios and total widths for the neutral ($h,H,A$) and charged
($H^\pm$) Higgs particles. We present total cross-sections and event rates for
the important discovery channels at the LHC and SSC. Promising physics
signatures are given by $h \to \gamma \gamma$, $H \to \gamma \gamma$ or $Z^*
Z^*$ or $\tau^+ \tau^-$, $A \to \tau^+ \tau^-$, and $t \to b H^+$ followed by
$H^+ \to \tau^+ \nu_{\tau}$, which should allow for an almost complete coverage
of the parameter space of the model.
