A simple, analytic model is presented that describes the steady state profile of anode nitrogen concentration in a polymer electrolyte membrane fuel cell operated with anode recirculation. The model is appropriate for fuel cells with straight gas channels and includes the effect of nitrogen crossover from cathode to anode through the membrane. The key analytic simplification in the model is that this crossover rate, when scaled to the gas flows in the channels, is small. This is a good approximation when the device is used at operating power levels. The model shows that the characteristic times for the anode nitrogen profiles to reach steady state are of the order of minutes and that the dilution effect of anode nitrogen is severe for pure recirculation. The model shows additionally that a small anode outlet bleed can significantly reduce the nitrogen dilution effect. Within the framework of the model, the energy efficiency of pure recirculation can be compared to hydrogen venting or partial anode bleeding. An optimal bleed rate is identified. The model and optimization analysis can be adapted to other fuel cell designs and operating conditions. Along with operating conditions, only two key parameters are needed: a nitrogen crossover coefficient and the marginal efficiency loss to compressors for increased anode stoichiometric gas flow. (C) 2011 Elsevier B.V. All rights reserved.