To provide a scavenging two-cycle engine which can enhance the function of acceleration and which can maximumly restrain deterioration of exhaust gas.

A stratiformly scavenging engine is composed of a scavenging passage 3 connecting a cylinder chamber 4a to a crank chamber 1a, an air passage connected to the scavenging passage 3, an air flow rate control means 12 for controlling the flow rate of air fed from the air passage 2 into the scavenging passage 3, a mixture flow passage 10 connected to the crank chamber 1a, and a mixture flow rate control means 11 for controlling the flow rate of mixture from the mixture flow passage 10 into the crank chamber 1a. Further, the air flow rate controlling means 12 is adapted to restric the flow rate of air during acceleration.