  For quantum theories with a classical limit (which includes the large N
limits of typical field theories), we derive a hierarchy of evolution equations
for equal time correlators which systematically incorporate corrections to the
limiting classical evolution. Explicit expressions are given for
next-to-leading order, and next-to-next-to-leading order time evolution. The
large N limit of N-component vector models, and the usual semiclassical limit
of point particle quantum mechanics are used as concrete examples. Our
formulation directly exploits the appropriate group structure which underlies
the construction of suitable coherent states and generates the classical phase
space. We discuss the growth of truncation error with time, and argue that
truncations of the large-N evolution equations are generically expected to be
useful only for times short compared to a ``decoherence'' time which scales
like N^{1/2}.
