The paper presents a general mathematical model for disperse systems in which direct interactions between particles are taken into consideration. The model is formulated in terms of transition measures, introduced on the basis of conditional Markov processes. The population balance equation, describing the behaviour of interactive populations, is developed in a general form of continuous and discontinuous terms. Moment equations are presented and analysed for the axial dispersion model with interparticle exchange processes of heat and mass. The applicability of the model is illustrated by applying it for describing a process of heating particles by gas with interparticle heat transfer, and a mass exchange process between fluid particles. (c) 2005 Elsevier Ltd. All rights reserved.