  We derive a kinetic equation with a non-Markovian collision term which
includes a memory effect, from Kadanoff-Baym equations in $\phi^4$ theory
within the three-loop level for the two-particle irreducible (2PI) effective
action. The memory effect is incorporated into the kinetic equation by a
generalized Kadanoff-Baym ansatz.Based on the kinetic equations with and
without the memory effect, we investigate an influence of this effect on decay
of a single particle excitation with zero momentum in 3+1 dimensions and the
spatially homogeneous case. Numerical results show that, while the time
evolution of the zero mode is completely unaffected by the memory effect due to
a separation of scales in the weak coupling regime, this effect leads first to
faster relaxation than the case without it and then to slower relaxation as the
coupling constant increases.
