We present a systematic approach to kinetic theory in homogeneous Newtonian cosmologies, which is based on a correlational picture of the cosmological principle. The compatibility of this approach with the more usual fluctuational picture is demonstrated by a derivation of the Layzer-Irvine equation from the BBGKY hierarchy. A kinetic-like equation, including the effects of collisions in the ‘ weak-coupling ’ approximation, is derived for the single-particle distribution describing an expanding universe. This equation differs from the standard equation in the adjunction to each binary interaction operator of an expansion factor, so that the effective interaction may be considered time dependent. It predicts the production of kinetic and thus also of correlational energy, in agreement with the fluctuational picture of cosmological clustering, where they can be compared.