The theory of Prigogine is applied to the deduction of a general kinetic equation for the singlet phase distribution for a fluid not in equilibrium. The intermolecular interaction is assumed to have the form of the sum of constituent pair forces; but the pair force itself is supposed to have a realistic form and any restriction to a hard-core repulsion is explicitly avoided. The general equation for the singlet distribution is set down in §5 and its derivation involves the consideration of the associated diagrams in numerical terms. The effects of the short-range (repulsive) and long-range (collective) molecular interactions are summed separately even although the hard-core repulsion of the pair potential is relaxed. The present paper is the natural extension of a previous communication by the present authors and of the earlier work of Rice and Allnatt.