  In the Minimal Supersymmetric Standard Model with complex parameters (cMSSM)
we calculate higher order corrections to the Higgs boson sector in the
Feynman-diagrammatic approach using the on-shell renormalization scheme. The
application of this approach to the cMSSM, being complementary to existing
approaches, is analyzed in detail. Numerical examples for the leading fermionic
corrections, including the leading two-loop effects, are presented. Numerical
agreement within 10% with other approaches is found for small and moderate
mixing in the scalar top sector. The leading fermionic corrections,
supplemented by the full logarithmic one-loop and the leading two-loop
contributions are implemented into the public Fortran code FeynHiggsFastC.
