The production mechanisms and decay modes of the heavy neutral and cha
rged Higgs bosons in the Minimal Supersymmetric Standard Model are inv
estigated at future e(+)e(-) colliders in the TeV energy regime. We ge
nerate supersymmetric particle spectra by requiring the MSSM Higgs pot
ential to produce correct radiative electroweak symmetry breaking, and
we assume a common scalar mass m(0), gaugino mass m(1/2) and trilinea
r coupling A, as well as gauge and Yukawa coupling unification at the
Grand Unification scale. Particular emphasis is put on the low tan bet
a solution in this scenario where decays of the Higgs bosons to Standa
rd Model particles compete with decays to supersymmetric charginos/neu
tralinos as well as sfermions. In the high tan beta case, the supersym
metric spectrum is either too heavy or the supersymmetric decay modes
are suppressed, since the Higgs bosons decay almost exclusively into b
and tau pairs. The main production mechanisms for the heavy Higgs par
ticles are the associated AH production and H+H- pair production with
cross sections of the order of a few fb.