Solid-state reactions generally start at specific sites, the first-formed product at these sites being referred to as "the nuclei". From a general law of nucleus formation, the simpler equations commonly encountered follow. Further reaction takes place at the interface between nuclei and reactant so that the first-formed nuclei grow in size. Visual observation of large nuclei shows that these grow at a constant rate, but in many solid-state decompositions, experimental evidence suggests a slower rate of growth for small nuclei, because the general kinetic equation based on nucleus formation and a constant rate of growth fails to adequately describe the early stages of the reaction before the rapid acceleratory process. The questions of long induction periods and the slower growth of nuclei at first are addressed, and a general phenomenological model is developed. This is applied To three different examples, and its applicability in three such varied cases suggests that it might prove to be of much wider use in reactions with long induction periods. In some reactions, structural changes induced by the reaction result in the multiplication ("branching") of nuclei and a general equation (of which the Prout-Tompkins equation is a special case) is derived. This general equation is shown to fit experimental data over a wider range than the original Prout-Tompkins equation.