Abstract: The invention provides the replacing of the known "macroscopic" processes by a "microscopic" approach control strategy for an NOx accumulator. The regeneration phases after approximately 30 seconds of a lean operation, which last approximately one second in the state of the art, is replaced by a rich operating cycle after a sequence of lean ones. The number of lean operating cycles which can be carried out before a regenerating operating cycle depends on the combustion process of the internal-combustion engine as well as on the construction and the volume of the catalyst.