It is intended to effectively prevent blow-by with no need for large changes in typical structures of two-cycle internal combustion engines. A main scavenging passage (24) for supplying air-fuel mixture from a crankcase to a combustion chamber for scavenging purposes has a branch scavenging passage (26) that extends upward aslant toward an intake port (14). The main scavenging passage (24) communicates with a first scavenging port (20) located nearer to an exhaust port (16). The branch scavenging passage (26) communicates with a second scavenging port (22). A mean cross-sectional area of the branch scavenging passage (26) is smaller than that of the main scavenging passage (24). Cross-sectional area of a portion (24b) next to an inlet port (24a) of the main scavenging passage (24) opening to the crankcase is smaller than the sum of cross-sectional areas of the first and second scavenging ports (20, 22).