An apparatus for the burning of solid particles, especially soot particles, separated from the exhaust gas from internal combustion engines has a rotationally symmetrical combustion chamber which coaxially adjoins an ignition burner connected with it by a flame transfer orifice. Fuel and air are metered to the ignition burner through an additional-air line and a fuel line and, as a prepared mixture, they are ignited in the ignition burner and enter the combustion chamber through a flame transfer orifice. In the combustion chamber an exhaust gas partial stream enriched with the solid particles is introduced, and, after the solid particles have been consumed together with the additional air put into the combustion chamber, the exhaust gas is then discharged again as cleaned exhaust together with the remaining combustion products through an outlet tube.