In this paper we present a transient, fully two-phase, non-isothermal model of carbon monoxide poisoning and oxygen bleeding in the membrane electrode assembly of a polymer electrolyte fuel cell. The model includes a detailed description of mass, heat and charge transport, chemisorption, electrochemical oxidation and heterogeneous catalysis (when oxygen is introduced). Example simulation results demonstrate the ability of the model to qualitatively capture the fundamental features of the poisoning process and the extent of poisoning with respect to channel temperature and concentration. Further examples show how the multi-step kinetics can interact with other physical phenomena such as liquid-water flooding, particularly in the anode. Carbon monoxide pulsing is simulated to demonstrate that the complicated reaction kinetics of oxygen bleeding can be captured and even predicted. It is shown that variations in the channel temperature have a convoluted effect on bleeding, and that trends in performance on relatively short time scales can be the precise opposite of the trends observed at steady state. We incorporate a bi-functional mechanism for carbon monoxide oxidation on platinum-ruthenium catalysts, demonstrating the marked reduction in the extent of poisoning, the effect of variations in the platinum-ruthenium ratio and the influence of temperature. Finally, we discuss the implications of the results, extensions to the model and possible avenues for experimental work.