A mathematical model that describes the transport of species in a multicomponent membrane is presented. The transport is described by concentrated-solution theory, and the electrochemical potential driving forces are described by a thermodynamic framework set forth in the first paper in this series. A kinetic model is developed to describe methanol oxidation kinetics on Pt-Ru catalysts. Physical properties are estimated by correlation of data in the literature and by simulation of methanol electrolysis experiments. This model provides the framework for direct methanol fuel cell simulation and design in the third paper in this series.