The method of dispersion relations has in recent years found a wide application for the study of elementary particle reactions. Most of the work, however, deals with reactions of the type [formula], while the theory of those with more than two particles in the final state is still in a very preliminary stage. One reason for this is that even with only three particles in the final state the theory is already much more complicated. Nevertheless, a further development of the theory seemed to us very desirable. The theory at present is being developed on various levels simultaneously. Generally speaking, the aim of this paper is to put the theory in a form as closely as possible analogous to Mandelstam's formulation of the theory of reactions of type [formula]. In the later sections we specialize on reactions [formula], but as much as possible the formulation is in more general terms.