  The dynamics of two-level systems in time-dependent backgrounds is under
consideration. We present some new exact solutions in special backgrounds
decaying in time. On the other hand, following ideas of Feynman, Vernon and
Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics
to a classical Hamiltonian system. This, in particular, opens the possibility
to directly apply powerful methods of classical mechanics (e.g. KAM methods) to
study the quantum system. Following such an approach, we draw conclusions of
relevance for ``quantum chaos'' when the external background is periodic or
quasi-periodic in time.
