The authors have been developing an empirical mathematical model to predict the dynamic behaviour of a polymer electrolyte membrane fuel cell (PEMFC) stack. Today there is a great number of models, describing steady-state behaviour of fuel cells by estimating the equilibrium voltage for a certain set of operating parameters, but models capable of predicting the transient process between two steady-state points are rare. However, in automotive applications round about 80% of operating situations are dynamic. To improve the reliability of fuel cell systems by model-based control for real-time simulation dynamic fuel cell stack model is needed. Physical motivated models, described by differential equations, usually are complex and need a lot of computing time. To meet the real-time capability the focus is set on empirical models. Fuel cells are highly nonlinear systems, so often used auto-regressive (AR), output-error (OE) or Box-Jenkins (BJ) models do not accomplish satisfying accuracy. Best results are achieved by splitting the behaviour into a nonlinear static and a linear dynamic subsystem, a so-called Uryson-Model. For system identification and model validation load steps with different amplitudes are applied to the fuel cell stack at various operation points and the voltage response is recorded. The presented model is implemented in MATLAB environment and has a computing time of less than 1 ms per step on a standard desktop computer with a 2.8 MHz CPU and 504 MB RAM. Lab tests are carried out at DaimlerChrysler R&D Centre with DaimlerChrysler PEMFC hardware and a good agreement is found between model simulations and lab tests. (c) 2007 Elsevier B.V. All rights reserved.