A two-dimensional mathematical model is developed for transport of multi-solute liquid (aqueous) solutions through reverse osmosis membranes in which strong affinity may exist between the membrane polymer and the solutes. The final objective of this research study is to predict the performance of reverse osmosis (RO) or nanofiltration (NF) membranes in the case of multi-solute aqueous systems in the presence of strong solute-membrane attraction. Modeling of membrane transport in this case is complex because of the interactions between solute, solvent and membrane. The model, which assumes a micro-porous structure for the membrane, is an extension of a single-solute model based on the preferential sorption-capillary flow mechanism, and takes detailed solute-solvent-membrane interactions into account. The model is believed to be the first to have been able to describe the anomalous behavior of such systems for multi-component aqueous solutions. The developed model is used to simulate the performance of cellulose acetate membrane in aqueous toluene-benzene systems by varying the operating pressure and mole fraction of toluene/benzene system. Generally, the separation of both solutes will decrease as the operating pressure is increased, with toluene having higher separations than benzene. The permeation flux also decreases with increasing operating pressure. However, the permeation flux of mixture increases as solutes concentration in feed solution is increased. The solutes separation values are higher at higher solutes concentrations of the feed. (c) 2005 Elsevier B.V. All rights reserved.