  Isotropization occurs on time scales much shorter than the thermal
equilibration time. This is a crucial ingredient for the understanding of
collision experiments of heavy nuclei or other nonequilibrium phenomena in
complex many body systems. We discuss in detail the limitations of estimates
based on standard ``linear'' or relaxation-time approximations, where
isotropization and thermal equilibration rates agree. For a weak-coupling
$\phi^4$-model the relaxation-time approximation underestimates the thermal
equilibration time by orders of magnitude, in contrast to the isotropization
time. The characteristic nonequilibrium isotropization rate can be enhanced as
compared to the close-to-equilibrium value. Our results are obtained from the
two-particle irreducible effective action, which includes off-shell and memory
effects and does not involve a gradient expansion. This allows us to determine
the range of validity of a description to lowest-order in gradients, which is
typically employed in kinetic equations.
