A device for selective oxidation of a substance stream comprises a selectively active catalyst. For improving the cold-starting characteristics, the device also has an oxidation catalyst that possesses high activity at low temperatures. The selectively active catalyst is applied as a coating onto one or more surfaces of interior walls of the device. A layer of oxidation catalyst is provided in at least the inlet region where the substance stream enters the device, between the layer of selectively active catalyst and the interior walls of the device.