  We begin with a discussion of the general form and general CP-- and CPT--
transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian
for the neutral kaon complex. Next, the properties of the exact effective
Hamiltonian for this complex are discussed. Using the Khalfin Theorem we show
that the diagonal matrix elements of the effective Hamiltonian governing the
time evolution in the subspace of states of an unstable particle and its
antiparticle need not be equal at for t > t_0 (t_0 is the instant of creation
of the pair) when the total system under consideration is CPT invariant but CP
noninvariant. The unusual consequence of this result is that, contrary to the
properties of stable particles, the masses of the unstable particle "1" and its
antiparticle "2" need not be equal for t >> t_0 in the case of preserved CPT
and violated CP symmetries. We also show that there exists an approximation
which is more accurate than the LOY, and which leads to an effective
Hamiltonian whose diagonal matrix elements posses properties consistent with
the conclusions for the exact effective Hamiltonian described above.
