A reciprocating piston engine (2) includes an exhaust system comprising an exhaust pipe (8) which communicates with a silencer (10), whose upstream portion (11) is divergent in the direction of gas flow through it, an oxidising catalyst (12) and an air supply pipe (14) communicating with the exhaust pipe at a position upstream of the catalyst and silencer. The air supply pipe (14) includes a Reed valve (16) which is adapted to open under a pressure differential to permit air to flow into the exhaust pipe. In order to maximise the air flow into the exhaust pipe the effect of pressure pulses within the exhaust pipe is utilised and for this purpose 3L2−(2L1+L2) is equal to ±0.25 to 0.5 m, wherein is the distance from the junction of the exhaust pipe (8) measured from a first intersection point at which the axes of the exhaust pipe (8) and the air supply pipe (14) intersect, to a point midway along the length in the flow direction of the said upstream portion (11) of the silencer (10) and L2 is the length of the air supply pipe (14) from the Reed valve (16) to the said first intersection point.