Аннотация:We deduce the most general nonlinear kinetic equation that describes the low-density limit of general Feller processes for systems of random numbers of classical particles with interaction, collisions, fragmentation and coagulation. This is done by studying the limiting (as ε → 0) evolution of Feller processes on U∪n=0∞ Xn with X = ℝd or X = ℤd described by generators of the form ε-1 ∑k=0K εk B(k), K ∈ N, where B(k) are the generators of k-nary interaction, whose general structure is also described in the paper.