The direct conversion of hydrogen into electricity by polymer membrane fuel cells (PEFC) is a promising option for future transportation and stationary energy supply systems. A model for heat and water transport in a polymer membrane fuel cell has been developed for evaluation with regard to structure and material. Moreover the dynamic simulation allows simulation of the transient state after changes of electrical load or gas flow rate and humidification. The polymer membrane fuel cell is subdivided into different components: gas distributor, gas diffusion layer, catalytic layer and membrane. Each of these components is described by a mathematical model which accounts for the physical phenomena arising in this structure: i.e. energy and mass transfer and electrochemical kinetics. In the simulation program each component is represented by a separate module. Coupling these modules results in a model describing a single electrode membrane unit or a complete fuel cell stack. Results are presented by current-voltage curves or temperature plots. The influence of model parameters such as thickness and porosity of the diffusion layer, or the structure of the catalytic layer, are shown. Furthermore, results of the dynamic behaviour of a polymer membrane fuel cell are presented.