  The interaction of an open system $\s$ with a pre- and post-selected
environment is studied. In general, under such circumstances $\s$ can not be
described in terms of a density matrix, {\it even when $\s$ in not
post-selected}. However, a simple description in terms of a two-state (TS) is
always available. The two-state of $\s$ evolves in time from an initially
`pure' TS to a `mixed' TS and back to a final `pure' TS. This generic process
is governed by a modified Liouville equation, which is derived. For a sub-class
of observables, which can still be described by an ordinary density matrix,
this evolution generates recoherence to a final pure state. In some cases
post-selection can even suppress any decoherence.
