  We consider the effective two-Higgs-doublet potential with complex
parameters, when the CP invariance is broken both explicitly and spontaneously.
Diagonal mass term in the local minimum of the potential is constructed for the
physical basis of Higgs fields, keeping explicitly the limiting case of
CP-conservation if the parameters are taken real. For special case of the
two-doublet Higgs sector of the minimal supersymmetric model, when CP
invariance is violated by the Higgs bosons interaction with scalar quarks of
the third generation, we calculate by means of the effective pothential method
the Higgs boson masses and evaluate the two-fermion Higgs boson decay widths
and the widths of rare one-loop mediated decays H -> \gamma \gamma, H -> gg.
