  We discuss the renormalization of the initial value problem in Nonequilibrium
Quantum Field Theory within a simple, yet instructive, example and show how to
obtain a renormalized time evolution for the two-point functions of a scalar
field and its conjugate momentum at all times. The scheme we propose is
applicable to systems that are initially far from equilibrium and compatible
with non-secular approximation schemes which capture thermalization. It is
based on Kadanoff-Baym equations for non-Gaussian initial states, complemented
by usual vacuum counterterms. We explicitly demonstrate how various
cutoff-dependent effects peculiar to nonequilibrium systems, including
time-dependent divergences or initial-time singularities, are avoided by taking
an initial non-Gaussian three-point vacuum correlation into account.
