The formalism of recombination statistics is extended in various directions. In the case of inter-band transitions, the conditions under which a recombination coefficient exists are investigated, and the effect of degeneracy of electron and hole gas is discussed. In the case of transitions in which traps participate, the formalism is extended to cover (a) degeneracy and (b) the case when impurity centres have several trapping levels. The more important special cases of the general formalism are considered. In all cases the possibility has been borne in mind that the departure from equilibrium may not be small.