  The conditions of quantum-classical correspondence for a system of two
interacting spins are investigated. Differences between quantum expectation
values and classical Liouville averages are examined for both regular and
chaotic dynamics well beyond the short-time regime of narrow states. We find
that quantum-classical differences initially grow exponentially with a
characteristic exponent consistently larger than the largest Lyapunov exponent.
We provide numerical evidence that the time of the break between the quantum
and classical predictions scales as log(${\cal J}/ \hbar$), where ${\cal J}$ is
a characteristic system action. However, this log break-time rule applies only
while the quantum-classical deviations are smaller than order hbar. We find
that the quantum observables remain well approximated by classical Liouville
averages over long times even for the chaotic motions of a few
degree-of-freedom system. To obtain this correspondence it is not necessary to
introduce the decoherence effects of a many degree-of-freedom environment.
