A two-cycle internal combustion engine comprises a cylinder head having two intake ports and an exhaust port opened to a combustion chamber, to which compresses fresh air is introduced via two intake valves. The intake and exhaust valves are operated in response to a crank angle. During an idling or light load running condition, an air control valve closes the second intake port. The exhaust valve is opened earlier than the second intake valve, and the first intake valve is opened later than the second intake valve, while the speed of the downward movement of the piston is relatively high. An exhaust gas swirl rotating around a cylinder axis is formed when the exhaust gas flows back into the condition chamber and the fresh air is slowly introduced via the first intake valve onto the exhaust gas swirl in the idling or light load condition. A large amount of fuel is rapidly introduced into the combustion chamber via the second intake valve in a heavy load condition.