  We solve the Kadanoff-Baym equations for nonequilibrium initial
configurations of the $\phi^4$-theory in 2+1 dimensions and compare to explicit
solutions of generalized transport equations for the same theory. The latter
transport equations are derived from the Kadanoff-Baym equation in a first
order gradient expansion in phase space and explicitly retain the off-shell
dynamics as inherent in the time-dependent spectral functions. The solutions of
these equations compare very well with the exact solutions of the full
Kadanoff-Baym equations with respect to the occupation numbers of the
individual modes, the spectral evolution as well as the chemical equilibration
process. Furthermore, the proper equilibrium off-shell distribution is reached
for large times contrary to the quasiparticle Boltzmann limit. We additionally
present a direct comparison of the solution of the generalized transport
equations in the Kadanoff-Baym and Botermans-Malfliet form; both solutions are
found to agree very well with each other.
