An adaptive model based monitoring strategy for a NOx trap catalyst is presented. First, a simplified model of the NOx trap is developed from a physical PDE (Partial Differential Equations) model. A validation on different types of data is given. Then two monitoring strategies are presented: a non-adaptive and an adaptive strategy, which uses a downstream EGO (Exhaust Gas Oxygen) sensor. The basic idea of the adaptive strategy is to put the catalyst and monitoring strategy in a particular condition such that a successive adaptation of three different parameters of the model is possible. The adaptive strategy is compared to the non-adaptive strategy by use of numerical simulations.