Abstract: A device for thermally or catalytically cleaning waste air containing combustible constituents including a combustion chamber, at least two receptacles containing heat storage mass for heating untreated gas before it is introduced into the combustion chamber and for heating the heat storage mass with cleaned gas from the combustion chamber, an untreated gas channel for feeding the untreated gas into the receptacles and a clean gas channel for discharging the clean gas from the receptacles. Each receptacle contains at least one inlet opening through which untreated gas is introduced into the receptacle from an untreated gas channel and at least one outlet opening through which cleaned gas is discharged from the receptacle into the clean gas channel. The inlet opening leads into a precombustion chamber between the inlet opening and the heat storage mass of the receptacle.