  In the context of the Minimal Supersymmetric extension of the Standard Model,
we discuss the impact of the decays of the neutral Higgs bosons into
supersymmetric particles, charginos/neutralinos and sfermions. We show that
these decay modes could be dominant, when they are kinematically accessible,
thus strongly suppressing the branching ratios for the decay channels which are
used to detect the Higgs bosons at hadron colliders. These SUSY decay modes
should therefore not be overlooked in the search for the Higgs particles at the
LHC.
