  We carry out a detailed analysis of the general two Higgs doublet model with
CP violation. We describe two different parametrizations of this model, and
then study the Higgs boson masses and the trilinear Higgs couplings for these
two parametrizations. Within a rather general model, we find that the trilinear
Higgs couplings have a significant dependence on the details of the model, even
when the lightest Higgs boson mass is taken to be a fixed parameter. We include
radiative corrections in the one-loop effective potential approximation in our
analysis of the Higgs boson masses and the Higgs trilinear couplings. The
one-loop corrections to the trilinear couplings of the two Higgs doublet model
also depend significantly on the details of the model, and can be rather large.
We study quantitatively the trilinear Higgs couplings, and show that these
couplings are typically several times larger than the corresponding Standard
Model trilinear Higgs coupling in some regions of the parameter space. We also
briefly discuss the decoupling limit of the two Higgs doublet model.
