  The proof of the Khalfin Theorem for neutral meson complex is analyzed. It is
shown that the unitarity of the time evolution operator for the total system
under considerations assures that the Khalfin's Theorem holds. The consequences
of this Theorem for the neutral mesons system are discussed: it is shown, eg.,
that diagonal matrix elements of the exact effective Hamiltonian for the
neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is
violated. Properties of time evolution governed by a time--independent
effective Hamiltonian acting in the neutral mesons subspace of states are
considered. Using the Khalfin's Theorem it is shown that if such Hamiltonian is
time--independent then the evolution operator for the total system containing
the neutral meson complex can not be a unitary operator. It is shown
graphically for a given specific model how the Khalfin's Theorem works. It is
also shown for this model how the difference of the mentioned diagonal matrix
elements of the effective Hamiltonian varies in time.
