  We consider the two-Higgs-doublet model with explicit CP-violation, where the
effective Higgs potential is not CP-invariant at the tree-level. Three neutral
Higgs bosons of the model are the mixtures of CP-even and CP-odd bosons which
exist in the CP-conserving limit of the theory. The mass spectrum and
tree-level couplings of the neutral Higgs bosons to gauge bosons and fermions
are significantly dependent on the parameters of the Higgs boson mixing matrix.
We calculate the Higgs-gauge boson, Higgs-fermion, triple and quartic Higgs
self-interactions in the MSSM with explicit CP-violation in the Higgs sector
and CP-violating Yukawa interactions of the third generation scalar quarks. In
some regions of the MSSM parameter space substantial changes of the
self-interaction vertices take place, leading to significant suppression or
enhancement of the multiple Higgs boson production cross sections.
