-In this paper, the observer based nonlinear state feedback controller has been developed to control the pressures of the oxygen and the hydrogen in the PEM(Proton Exchange Membrane) fuel cell system. Nonlinear model of the PEM fuel cell system was introduced to study the design problems of the state observer and model based controller. A cascade observer using the filtering technique was used to estimate the pressure derivatives of the cathode and the anode in the system. In order to estimate the pressures of the cathode and the anode, the sliding mode observer was designed by using these pressure derivatives. To estimate the oxygen pressure and the hydrogen pressure in the system, the nonlinear state observer was designed by using the cathode pressure estimates and the anode it. These results will be very useful to design the state feedback controller. The validity of the proposed observers and the controller has been investigated by using the Lyapunov's stability analysis strategy.