An exhaust system of an internal combustion engine includes a first filter device and a second filter device located downstream of the first. Both filter devices filter soot particles out of the exhaust gas. At least the first filter device has a catalytic material, which promotes an exothermic soot burnoff in such a way that as a result of the corresponding heating up of the exhaust gas, the soot burnoff in the second filter device is set in motion. The materials of the two filter devices are selected such that the soot burnoff in the first filter device ensues at a lower temperature and/or at a similar temperature is stronger than in the second filter device.