The basic concepts of a distributional theory of nonsteady-state continuous-flow processes are described in terms of standard language and notation of modern probability theory and stochastic processes. These concepts are used in more precise characterizations of residence time distributions and of the extreme states of microscopic mixing. While Zwietering's concept of maximum mixedness is not ambiguous, certain ambiguities in the concept of complete segregation suggest two separate mixing states, called minimum mixedness and maximum segregation, that are each opposite to maximum mixedness in a certain sense. These are characterized and used to derive a method for computing the extent of chemical reaction for arbitrary kinetics in a reactor with each extreme of mixing and with nonsteady, nonhomogeneous feed streams.