The distribution functionals that are encountered in the Bogoliubov formalism for systems in the kinetic stage are replaced by the correlation functionals in a manner similar to the ones that are familiar in the cluster expansion series. The equation satisfied by these functionals is derived for the case when the interaction potential is binary. It is shown that the analytic solution of this equation subject to Bogoliubov's initial condition is of order λs−1 where λ is the interaction parameter and s is the number of particles involved in the correlation functional under consideration. This property enables one to break the hierarchy even if one keeps the terms of all orders in nλ, n being the density, as is the usual procedure for plasmas.