A two-cycle internal combustion engine comprises a cylinder head having an intake port and two exhaust ports opened to a combustion chamber, to which compressed fresh air is introduced via an intake valve. The intake valve and two exhaust valves are operated in response to a crank angle. One of the exhaust valves is opened earlier than the other exhaust valve and the intake valve when the speed of the downward movement of the piston is relatively high, such that a part of exhaust gas in the one exhaust port flows back to the combustion chamber in that condition. An exhaust gas swirl rotating around a cylinder axis is formed when the exhaust gas flows back and the fresh air is slowly introduced onto the exhaust gas swirl in that condition.