Fuel cell stack systems are under intensive development for mobile and stationary power applications. In particular, Proton Exchange Membrane (PEM) Fuel Cells (also known as Polymer Electrolyte Membrane Fuel Cells) are currently in a more mature stage for ground vehicle applications. This paper proposes a theoretical innovative approach to the analysis of the electrochemical transient behavior (anode-cathode). The transient behavior due to the electrochemical dynamic may impact the behavior of the resulting load current. Boundary conditions influence the resulting electric field, the boundary condition are strongly depending of H2 and O2 physical parameters. Maxwell's equations are used in order to describe the model. Solutions through dyadic harmonic wavelets at different levels of resolution are presented. Wavelets approach, through their different space-time levels of resolution, can favorable describe the segmented space structure of the stack. In the meantime, transient dynamic inside of the stack can be adaptively studied. An outlook closes the paper. © Springer-Verlag Berlin Heidelberg 2006.