Nonlinear processes present difficult problems in extrapolating toxicological kinetics from one dose or species to another. A model that includes the details of these processes will aid in identifying those conditions under which a linear extrapolation is not valid. Previously, a kinetic model of the perfused rat liver system was presented that included the effects of equilibrium protein binding, diffusion-based and saturable membrane transport, metabolism, and biliary excretion. This model has been extended here to account for two complex processes. First, the kinetics of chemical association and dissociation from binding sites in various compartments are explicitly included to allow for the possibility that the binding of the compound is not in equilibrium. Second, mediated transport via a simple four-state carrier in the membrane has been included at both the sinusoidal and biliary membranes of the liver cell. This enables inclusion of carrier-specific transport processes (such as selective transport against a concentration gradient) in modeling the kinetics in perfused rat liver experiments. Simulations demonstrating the effects of each of these processes on observable state variables have been conducted. Physiological conditions that elicit nonlinear behavior have been identified.