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Correctly controlling a fuel cell system and maintaining correct operating conditions, particularly under dynamic load variations, is difficult without advanced, multivariable control systems. In order to design and implement such controllers, an appropriate fuel cell system model is required. This paper proposes such a model for a PEMFC fuel cell system running on gaseous hydrogen and a non-pressurised air supply. The model is composed of a steady-state fuel cell stack model that links the operating conditions (e.g. air flow rate, hydrogen pressure, electrical current, etc.) to the fuel cell stack’s electrical voltage. This is complemented by a dynamic, steady state model for the auxiliary systems responsible for maintaining the above operating conditions as a function of the user’s interaction. Combining the two models yields an overall, dynamic fuel cell system model that can be used as a basis for implementing advanced control strategies.