  The problem of renormalization of the semiclassical one-loop equations used
in the non-equilibrium field theory is considered. Recently, the
renormalizability of such equations has been justified for some special cases
of classical field configurations. In this paper the general case of arbitrary
spatially inhomogeneous field configuration is investigated. It is shown that
for certain quantum states the divergences arising in one-loop equations can be
eliminated by usual perturbation-theory counterterms.
