  We construct asymptotic expansions of Laplace type for the time-dependent
quantum averages for Bose systems with many degrees of freedom, initially
populated in coherent states. These solutions are localized in phase space, and
they are different from the usual oscillating asymptotics for the
quasi-classical wave functions. These expansions are valid on any fixed time
interval, and caustics do not contribute to the asymptotics.
