The PEM fuel cell is a device which generates electricity from a chemical reaction between hydrogen and oxygen. The PEM fuel cell requires many ancillaries to operate the system. A control system is needed to optimize the performance of the PEMFC. This thesis is focused upon three specific control problems related to PEM fuel cell systems. The first problem is the control of the air (oxygen source) entering in the cathode side of fuel cell. The objective is to regulate the oxygen excess ratio in order to maintain the optimum net power output. This problem has been addressed using nonlinear second order sliding mode controllers, which are robust against parametric uncertainty and external disturbance. The SOSM controllers are based on two algorithms: sub-optimal and adaptive Super Twisting. Their performance is validated through Hardware In Loop simulation. The second problem is to maintain the centrifugal compressor in its operating zone, while avoiding the oxygen starvation in the cathode side during rapid load variations. The proposed solution to this problem is a load governor, which is similar to a variable bandwidth first order linear filter. Two adjustment algorithms have been applied for the bandwidth coefficient, based on the Extremum Seeking technique. Their performance has been validated experimentally. The third problem addressed in this thesis is the regulation of the pressure difference between the anode and the cathode during load variations. The control objective is achieved using second order sliding mode MIMO controller, which has been shown to be robust against parametric uncertainty and external disturbance.