It is perhaps surprising that if we know only that a process is accomplished by two or more functionally distinct subprocesses carried out in stages with stochastically independent durations, then we also know about some of the properties of the durations of that process. In particular, we know about aspects of the distributions of those durations and combinations of them. This chapter describes some of these properties. They bear on whether the reaction-time (RT) distribution from the different conditions in a factorial experiment can have the same shape, and on the conditions under which the popular ex-Gaussian distribution can describe RT distributions.