Transport models are developed for diffusion with self-association or intersolute solvation through a membrane. Permeation breakthrough is defined as the time at which a specified amount of penetrant has accumulated downstream of the membrane. Numerical solutions for the transient portion of the cumulative flux expression are used to determine the effect of association or solvation on the breakthrough time. At low fractions of unassociated or unsolvated penetrant at the upstream surface, the breakthrough time increases with decreasing mobility of the associated or solvated species. However, the effect of finite kinetics results in breakthrough times that are either greater or less than those at local equilibrium depending on the mobility of the associated or solvated species. These results are discussed in terms of local sources and sinks of penetrant. For materials of equivalent penetrant solubilities, those in which the equilibrium strongly favors the formation of immobile dusters or complexes will have measurably longer breakthrough times.