The current-potential curves of polymer electrolyte membrane (PEM) fuel cells exhibit under certain conditions steady-state multiplicity, i.e. for a fixed current value, there are two corresponding cell potential values and thus the current versus potential curve exhibits a local maximum. This behaviour cannot be described by any of the known classical mathematical expressions for overpotential. We have studied this phenomenon in PEM fuel cells operating on H-2 with Pt cathodes and Pt-Ru- or C-based anodes and have found that the steady-state multiplicity results from the significant dependence of the Nation membrane conductivity on cell potential. A simple mathematical model accounting for this non-linear behaviour of Nation conductivity describes semi quantitatively the results both of the present work and of previous literature studies, where the current-potential curves exhibit either steady-state multiplicity or a significant downward bending of the current-potential curve. The role of the non-linear Nafion membrane conductivity in the current and potential oscillations observed in presence of CO at the anode is also briefly discussed together with its implications about the proton transfer mechanism in the Nation membrane. (C) 2005 Elsevier Ltd. All rights reserved.