  Propagation of the Wigner function is studied on two levels of semiclassical
propagation, one based on the van-Vleck propagator, the other on phase-space
path integration. Leading quantum corrections to the classical Liouville
propagator take the form of a time-dependent quantum spot. Its oscillatory
structure depends on whether the underlying classical flow is elliptic or
hyperbolic. It can be interpreted as the result of interference of a
\emph{pair} of classical trajectories, indicating how quantum coherences are to
be propagated semiclassically in phase space. The phase-space path-integral
approach allows for a finer resolution of the quantum spot in terms of Airy
functions.
