  Motivated by the recent experimental announcements for direct measurements of
time-reversal non-invariance in the neutral kaon system, we make a comparative
discussion of the CPLEAR and KTeV measurements. The most suitable way to
consistently incorporate the mixing, the time evolution and the decays of
kaons, is to describe the neutral kaon system as a system with a non-Hermitean
Hamiltonian. In this framework, the physical (decaying) incoming and outgoing
states are distinct and belong to dual spaces. Moreover, since they are
eigenstates of the full Hamiltonian, they never oscillate. This is directly
manifest in the orthogonality conditions of the physical states, which entirely
determine the evolution of the kaon system. Along these lines we conclude:
CPLEAR studies K0-bar{K0} oscillations, a process where initial and final
states can be reversed, the CPLEAR asymmetry being an effect directly related
to the definition of time-reversal. Conclusively, CPLEAR provides a direct
measurement of T-violation without any assumption either on unitarity or on
CPT-invariance. The KTeV experiment studies in particular the process KL -> pi+
pi- e+ e- where they measure a T-odd effect. However, using unitarity together
with estimates of the final state interactions, it should be possible to
determine whether this effect can be identified with a genuine T-reversal
violation.
