For a NOx trap catalyst to work properly, it is important that the times for the lean period and the rich spikes are correctly calculated in the engine management system (EMS). This paper deals with the development of a physically based NOx trap model for implementation in the EMS. The catalyst was divided into different segments (complete mixed cells) to correctly mimic the axial distribution of stored NOx and the axial temperature profile. Furthermore, the model included physical steps as adsorption, desorption, storage and release of NOx. The model also includes the storage and reduction of O2 and a simplified model of the heat release from the oxidation of the reductants. The model could successfully describe the process of storage and release in a short time interval. However, problems to describe the function of the NOx trap occurred after longer time in the vehicle because of inaccurate estimation of the input variables. Results are presented from experiments in synthetic exhausts, engine bench and vehicle testing.