Abstract: A two-stroke internal combustion engine comprising a cylinder head 14 having combustion chambers 18 with two intake valves 24 and two exhaust valves 26 arranged therein. Two intake manifolds 30 and 32, respectively, have branch pipes connected to each respective intake port 24. An intake control valve 48 l is arranged in one of the manifold 32, which closes at idling and under a low load of the engine. Further, a swirl S is generated about an axis of the combustion chamber 18 by a portion of exhaust gas caused to flow back from the exhaust ports 22 into the combustion chamber 18 after being once exhausted through the exhaust ports when the exhaust valves are opened, resulting in a two layered stratification in the combustion chamber between fresh air and remaining exhaust gas. A supply of fuel causees a further three layered stratification among a fuel mixture, fresh air, and burned gas, by supplying fuel at alternating cycles of the engine when the engine is under a low load.