In this paper, a non linear control strategy is applied to the air supply subsystem of a polymer electrode membrane fuel cell (PEMFC). Based on a simplified control model and using the differential flatness control theory, a controller is designed in order to regulate the most important variables in the air supply subsystem: the oxygen stoechiometry and the cathode pressure. Simulations are made using a very detailed model validated experimentally, which allows the evolution of different state variables in the stack to be observed during the power deliver operation. The simulation results show that the controller gives a good response in terms of performance, robustness and durability of the system, despite the dynamics power profiles demanded, the approximations made and the disturbances.