A stepped piston engine comprises first (10), second (11) and third (12) stepped cylinders, each cylinder (10, 11, 12) having a larger diameter pumping part (10p, 11p, 12p), and a smaller diameter working part (10w, 11w, 12w), and a piston (13, 14, 15) slidable in the cylinder, each piston (13, 14, 15) being coupled to an output shaft (16) of the engine, first transfer passage means (20) to transfer the precompressed charge from the larger diameter pumping part (10p) of the first cylinder (10) to the smaller diameter working part (11w) of the second cylinder (11), second transfer passage means (21), to transfer precompressed charge from the larger diameter pumping part (11p) of the second cylinder (11) to the smaller diameter working part (124) of the third cylinder (12), and third transfer passage means (22) to transfer precompressed charge from the larger diameter pumping part (12p) of the third cylinder (12) to the smaller diameter working part (10w) of the first cylinder (10).