This paper has developed a complete two-phase model of a proton exchange membrane (PEM) fuel cell by considering fluid flow, heat transfer and current simultaneously. In fluid flow, two momentum equations governing separately the gaseous-mixture velocity (u(g)) and the liquid-water velocity (u(w)) illustrate the behaviors of the two-phase flow in a porous electrode. Correlations for the capillary pressure and the saturation level connect the above two-fluid transports. In heat transfer, a local thermal non-equilibrium (LTNE) model accounting for intrinsic heat transfer between the reactant fluids and the solid matrices depicts the interactions between the reactant-fluid temperature (T-f) and the solid-matrix temperature (T-s). The irreversibility heating due to electrochemical reactions, Joule heating arising from Ohmic resistance, and latent heat of water condensation/evaporation are considered in the present non-isothermal model. In current, Ohm's law is applied to yield the conservations in ionic current (i(m)) and electronic current (i(s)) in the catalyst layer. The Butler-Volmer correlation describes the relation of the potential difference (overpotential) and the transfer current between the electrolyte (such as Nation (TM)) and the catalyst (such as Pt/C). (c) 2006 Elsevier B.V. All rights reserved.