A one-dimensional rigorous process model of a single-cell direct methanol fuel cell (DMFC) is presented. Multi-component mass transport in the diffusion layers and the polymer electrolyte membrane (PEM) is described using the generalised Maxwell–Stefan (MS) equation for porous structures. In the PEM, also local swelling behaviour and non-idealities are accounted for by a Flory–Huggins model for the activities of the mobile species inside the pores of the PEM. Phase equilibria between the pore liquid inside the PEM and those inside the pores of both catalyst layer are formulated based on literature data and activity models. Although two-phase behaviour in both diffusion layers is neglected, the model shows good agreement to own experimental data over a wide range of operating conditions, with respect to methanol and water crossover fluxes as well as to current–voltage characteristics. Only for very low current densities and in the limiting current regime significant deviations between model and experiments are found.