  Assuming a light Higgs boson is discovered, its nature may remain unknown in
case that no supersymmetric particles are found. The detection and study of
heavier Higgs particles is then of great interest. For this purpose the
Compton-collider option of a high energy e+e- linear collider is optimal both
to produce Higgs bosons and to reveal their CP-parity. Assuming realistic
photon luminosities for various configurations of laser and linac
polarizations, we study the heavy, neutral MSSM Higgs signals for the most
relevant decay modes as well as their corresponding backgrounds. The MSSM H and
A Higgs bosons with masses up to a ~80% of the linac c.m.s. energy may be
observed and their CP-parity tested for Higgs masses ~450 GeV, at the
gamma-gamma mode of a ~1 TeV linear collider.
