The present invention relates to an exhaust-gas aftertreatment system which comprises a preferably catalytically active particle filter (wall-flow filter) which is followed in turn by a throughflow monolith (flow-through monolith) which is preferably provided with a catalytically active function. Both components have the same storage functions for gaseous substances present in the exhaust gas of internal combustion engines. The system is suitable in particular for the simultaneous removal of particles and pollutants from the exhaust gas of both predominantly lean-operated internal combustion engines and also of internal combustion engines operated predominantly with a stoichiometric air/fuel mixture. Likewise described is a process for the production and the use of such a system for exhaust-gas aftertreatment.