A four-stroke engine (1) structured to introduce fresh air and EGR gas into a cylinder (1a) includes a blowdown supercharging system (40) using a combustion chamber internal pressure when exhaust valves open in an expansion stroke of a first cylinder (hereinafter denoted as an exhaust blowdown pressure) for introducing EGR gas into a second cylinder from near a bottom dead center of an intake stroke to near a bottom dead center of a compression stroke of the second cylinder which is different from the first cylinder in combustion timing, and a secondary air supply system (20) supplying secondary air to an exhaust port (1e) of the second cylinder prior to arrival of the exhaust blowdown pressure at the second cylinder. The secondary air in the exhaust port and the EGR gas are supercharged into the second cylinder by the exhaust blowdown pressure from the first cylinder.