A two-stroke engine comprises a cylinder (2) accommodating a piston (6) and having an air inlet port (18) and an exhaust port (14,16). The exhaust port (14,16) communicates with an exhaust system (25) which includes a reduction catalyst (R) and an oxidation catalyst (O). The exhaust system (25) includes two exhaust flow paths (24,26) in parallel, the first (24) of which includes the reduction catalyst (R) and the second of which bypasses the reduction catalyst (R), the downstream ends of the two flow paths (24,26) being connected together upstream of the oxidation catalyst (O). The exhaust port (14,16) is controlled by the piston (2) or by poppet valves (32,34) so that as the piston (6) performs its downstroke the initial flow of exhaust gas is substantially through the first flow path (24) and the subsequent flow of exhaust gas is substantially through the second flow path (26).