A "general" model of membrane transport was formulated using the mechanistic Maxwell-Stefan approach and generalized driving forces, which included the contribution from the various internal and external driving forces. Transient models of dialysis and pervaporation were developed that used exactly the same general model to describe the transport through the membrane. In this model, the bulk solution/polymer equilibria were described by a modified Flory-Huggins model, and the concentration dependence of ternary Maxwell-Stefan diffusivities was described by a natural extension of the binary Vignes relationship to a multicomponent system. A notable advantage of the general model lies in the fact that the Maxwell-Stefan diffusivities retain their physical significance irrespective of the number of components present. This offers the opportunity of recovering many of the model parameters from relatively simple binary experiments. The results obtained indicate that the general model is capable of describing the transient dialysis and pervaporation of the {ethanol-water}/silicone rubber system with an identical set of concentration dependent equilibrium and diffusive parameters. The general model provides a solid framework for the theoretical description of diverse processes employing a nonporous polymer as the selective separation barrier.