The performance equations for cathodes of polymer electrolyte fuel cells (PEFCs) that describe the dependence of cathode potential on current density are developed. Formulation of the performance equations starts from the reduction of a one-dimensional model that considers, in detail, the potential losses pertinent to the limitations of electron conduction, oxygen diffusion, proton migration, and the oxygen reduction reaction. In particular, non-uniform accumulation of liquid water in the gas diffuser, which partially blocks the gas channels and imposes a greater resistance for oxygen transport, is taken into account. Reduction of the one-dimensional model is implemented by approximating the oxygen concentration profile in the catalyst layer with a parabolic polynomial or a piecewise parabolic one determined by the occurrence of oxygen depletion. The final forms of the equations are obtained by applying the method of weighted residuals over the catalyst layer. The weighting function is selected in such a way that the weighted residuals can be analytically integrated. Potential losses caused by the various limiting processes can be quantitatively estimated by the performance equations. Thus, they provide a convenient diagnostic tool for the cathode performance. Computational results reveal that the performance equations agree well with the original one-dimensional model over an extensive range of parameter values. This indicates that the present performance equations can be used as a substitute for the one-dimensional model to provide quantitatively correct predictions for the cathode performance of PEFCs. (C) 2004 Elsevier B.V. All rights reserved.