  In the present article we consider some general class of divergent diagrams
in Keldysh diagram technique. These divergences arise for nonequilibrium matter
and closely related to the divergences in the kinetic theory of gases. We
suggest a scheme of renormalization of such divergences and illustrate it on
some examples. In the other papers of these series we develop the general
theory of renormalization of nonequilibrium diagram technique. The fact that
thermal divergences in non-equilibrium diagram technique can be renormalized
leads to the following consequence: to prove that the system tends to the
thermal equilibrium one should to take into account the behaviour of the system
on its boundary. In this paper we illustrate this fact on Bogoliubov derivation
of kinetic equations.
