  Using the prescription of the nonequilibrium statistical operator method, we
derive a non-Markovian generalization to the kinetic theory described by Walser
{\sl et al.} [Phys. Rev. A {\bf 59}, 3878 (1999)]. Quasi-particle damping and
effects arising from the finite duration of a collision are introduced to
include terms beyond the Born approximation. Such a self-consistent theory is
shown to conserve energy to second order in the interaction strength, even in
the Markov limit. This kinetic theory is applied to a simple model of a Bose
gas confined in a spherical trap to study the full real-time evolution towards
equilibrium. A modified form for the damping function, is seen to strongly
improve the energy conservation. Based on a linear response calculation, we
predict the damping rates and frequencies of the collective excitations. We
demonstrate the emergence of differing time scales for damping and
equilibration.
