  We investigate unitarity bounds in the most general two Higgs doublet model
without a discrete $Z_2$ symmetry nor CP conservation. S-wave amplitudes for
two-body elastic scatterings of Nambu-Goldstone bosons and physical Higgs
bosons are calculated at high energies for all possible initial and final
states (14 neutral, 8 singly-charged and 3 doubly-charged states). We obtain
analytic formulae for the block-diagonalized scattering matrix by the
classification of the two body scattering states using the conserved quantum
numbers at high energies. Imposing the condition of perturbative unitarity to
the eigenvalues of the scattering matrix, constraints on the model parameters
can be obtained. We apply our results to constrain the mass range of the
next--to--lightest Higgs state in the model.
