  We study the role of time-reversal symmetry on the dynamical response of
nonlinear optical systems that behave as unidirectional ("one-way") devices. It
is shown that lossless nonlinear materials, despite being nonreciprocal, are
typically time-reversal invariant. This property raises an apparent paradox
because time-reversal invariant systems are forcibly bi-directional. Here, we
present a solution for this conundrum, and theoretically explain why the
"one-way" behavior can indeed be compatible with the time-reversal invariance.
It is found that in the time-reversed problem the incident waves have a
variation in time that is generally incompatible with the adiabatic
approximation. Due to this reason the adiabatic approximation fails to predict
the bi-directional nature of nonlinear system. We discuss the implications of
this finding in the performance of practical nonlinear "one-way" devices.
