This paper is an elaborate generalization of the author’s previously developed theory of partially elastic collisions and gravitational encounters of planetesimals in an arbitrary gravitational field [the author, Moon Planets, 28, 267-303 (1983; Zbl 0527.70012)]. The present generalization takes account of particles with different characteristics (mass, internal density, elastic parameters, electric charge, etcetera), the evolution of which is governed by an extra set of (coupled) first- order differential equations. The theory is developed much along the same lines as before. Having arrived at the complicated set of complete equations, the author specializes to an approximate potential for an axially symmetric disc around a central body. The numerical results which are obtained for equilibrium states are found to be in good agreement with computer simulations of Keplerian systems, performed by H. Salo and J. Lukkari [Earth, Moon and Planets 30, 229-274 (1984)].