Exhaust-gas aftertreatment system for internal combustion engines, having a wall-flow filter as component (1) and, downstream thereof, a flow-through monolith as component (2), with both components (1) and (2) having at least one storage function for the same compound, selected from the group consisting of SOx, NOx, NH3, O2, HC, and H2S, which is present in the exhaust gas, wherein
- the storage capacity in the component (2) is to be designed such that the breakthrough signal downstream of component (2) has the highest gradient of the concentration curve resulting at the respective termination criterion taken into consideration for the exhaust-gas compound while as little as possible of the storage material is used.