Abstract: A reactor for the oxidation of unburned and partially burned components in the exhaust gas from an internal combustion engine comprising a chamber which is substantially circular in cross-sections perpendicular to its axis, one or more inlet pipes which pass a mixture of exhaust gas and air substantially tangentially into the chamber near to one end thereof, and an outlet pipe near to the other end of the chamber and which is so arranged that exhaust gas leaves the chamber substantially tangentially. The tangential inlet and tangential outlet of gases minimizes energy losses in the gas passing through the reactor. The ratio of the cross-sectional areas of the inlet pipe(s) to reactor chamber is preferably from 1:9 to 25:36, and similar ranges of cross-sectional area ratios are preferred for the outlet pipe and chamber. The ratio of the length of the reaction chamber to diameter is preferably from 1:1 to 4:1.