The theoretical description of multicomponent transport across nonporous polymeric membranes was investigated using two alternative frameworks: the phenomenological approach of irreversible thermodynamics and the mechanistic Stefan-Maxwell formulation. The transport models developed account for potential equilibrium and/or kinetic coupling of fluxes and the contribution of diffusion induced non-selective flow within the polymer. The models were validated against transient dialysis and pervaporation data for the {ethanol-water}/silicone rubber system. A critical assessment was obtained by recovering the model parameters from the dialysis data and using the same parameters to predict the transient pervaporation performance. An empirical modification of the Flory-Huggins model was developed to describe the sorption of small polar solutes into hydrophobic membranes, which provided a physically realistic description of the sorption equilibria for the {ethanol-water}/silicone rubber system. The irreversible thermodynamics approach was used to develop transient models of dialysis and pervaporation. Average phenomenological diffusion coefficients recovered from dialysis data can give a good qualitative prediction of pervaporation performance. However, a quantitative prediction requires the explicit inclusion of the concentration dependence of the diffusivities, which is best achieved within the mechanistic Stefan-Maxwell formulation. A generic model of membrane transport was formulated using the mechanistic Stephan-Maxwell approach and generalised driving forces, which included the contribution from the various internal and external driving forces. The results obtained indicate that the generic 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.