A two-stroke internal combustion engine comprising a cylinder head 14 having intake valves 20 and exhaust valves 22 arranged therein. A supercharger 42 is arranged in an intake pipe 44 and a tank 46 is mounted downstream of the supercharger 42. A valve 48 is arranged in an opening between the tank 46 and the pipe 44. From the pipe b 44, two intake manifolds 30 and 32 are branched, with respective branch pipes connected to the respective intake ports 24. An intake control valve 50 is arranged in one of the manifold 32, which closes at idling and under a low load of the engine. The engine further has means for generating a swirl S about an axis of the combustion chamber 18 by a portion of exhaust gas caused to flow back from the exhaust port 26 into the combustion chamber 18 after being once exhausted through the exhaust port when the exhaust valve is open.