Described is a method for cleaning the exhaust gases of internal combustion engines, which method is suitable for reducing harmful gases and particle emissions. Here, the exhaust gas to be cleaned is conducted, under operating conditions, with a discontinuous profile of the air ratio λ across a wall-flow filter substrate which comprises a catalytically active coating containing one storage material. The storage material is suitable for temporarily storing one or more exhaust-gas components under certain operating conditions and releasing said exhaust-gas components again in a targeted fashion in the event of a suitable change in the operating conditions. The coating is configured such that the component has a gradient of the storage material concentration and/or of the total coating amount, with the highest concentration of the storage material in the longitudinal direction of the component being present on the inflow side. At least 60% by weight of the storage material in relation to its total amount is present in the walls between inflow and outflow ducts, and at least 50% by weight of the storage material in relation to its total amount is present in a first, inflow-side zone in the wall-flow filter substrate.