Hydrogen from water electrolysis associated with renewable energies is one of the most attractive solutions for the green energy storage. To improve the efficiency and the safety of such stations, some technological studies are still under investigation both on methods and materials. As methods, control, monitoring and diagnosis algorithms are relevant tools. These methods are efficient when they use an accurate mathematical model representing the real behaviour of hydrogen production system. This work focuses on the dynamical modelling and the monitoring of Proton Exchange Membrane (PEM) electrolyser. Our contribution consists in three parts: to develop an analytical dynamical PEM electrolyser model dedicated to the control and the monitoring; to identify the model parameters and to propose adequate monitoring tools. The proposed model is deduced from physical laws and electrochemical equations and consists in a steady-state electric model coupled with a dynamical thermal model. The estimation of the model parameters is achieved using identification and data fitting techniques based on experimental measurements. Taking into account the information given by the proposed analytical model and the experimentation data (temperature T, voltage U and current I) given by a PEM electrolyser composed of seven cells, the model parameters are identified. After estimating the dynamical model, model based diagnosis approach is used in order to monitoring the PEM electrolyser and to ensure its safety. We illustrate how our algorithm can detect and isolate faults on actuators, on sensors or on electrolyser system.