Abstract: A method for estimating the degradation of the trapping capacity of a NOx-Trap catalytic converter, in accordance with which, if the actual duration of a first NOx regeneration process is equal to the predetermined duration, it is assumed that the trapping capacity is unchanged; if the actual duration of the first NOx regeneration process is less than the predetermined duration, at least one corrective action is performed in order to attempt to counteract the degeneration of the NOx-Trap catalytic converter, a subsequent NOx regeneration process is performed, if the actual duration of the subsequent NOx regeneration process is equal to the predetermined duration, then new characteristic operating parameters for the corrective action are used for the subsequent life of the NOx-Trap catalytic converter whereas, if the actual duration of the subsequent NOx regeneration process is less than the predetermined duration, the estimated trapping capacity of the NOx-Trap catalytic converter is reduced.