  We present a detailed study of the decays of the Higgs bosons $H^+$, $H^0$,
and $A^0$ within the Minimal Supersymmetric Standard Model including SUSY--QCD
corrections. We find that the supersymmetric modes $\tilde t \bar{\tilde b}$
($\tilde t \bar{\tilde t}$, and for large $\tan\beta$ $\tilde b \bar{\tilde
b}$) can dominate the $H^+$ ($H^0$, $A^0$) decays in a wide range of the model
parameters due to the large Yukawa couplings and mixings of $\tilde t$ and
$\tilde b$. Compared to the conventional modes $H^+ \to \tau^+ \nu_{\tau}, t
\bar b$, and $H^0, A^0 \to t \bar t, b \bar b$, the supersymmetric modes can
have an important impact on the Higgs boson searches at future colliders.
