We consider the evolution of particle segregation in collisional flows of two types of spheres down rigid bumpy inclines in the absence of sidewalls. We restrict our analysis to dense flows and use an extension of kinetic theory to predict the concentration of the mixture and the profiles of mixture velocity and granular temperature. A kinetic theory for a binary mixture of nearly elastic spheres that do not differ by much in their size or mass is employed to predict the evolution of the concentration fractions of the two types of spheres. We treat situations in which the flow of the mixture is steady and uniform, but the segregation evolves, either in space or in time. Comparisons of the predictions with the results of discrete numerical simulation and with physical experiments are, in general, good.