A power unit for a motorcycle having a continuously variable transmission, which is housed in a transmission chamber inside a engine body and which accomplishes stepless changes in the transmission of power from a drive pulley shaft to a driven pulley shaft by changing the effective diameter with which a belt actually wraps around each of the drive and the driven pulleys. An input clutch is set between a crankshaft and a drive pulley and is provided on the drive pulley shaft. A starter clutch is set between a driven pulley shaft and a rear wheel and is provided on the driven pulley shaft. The switching between the engagement and disengagement of one of the input clutch and the starter clutch is hydraulically controlled. Meanwhile, the switching between the engagement and disengagement of the other one of the input clutch and the starter clutch is mechanically controlled.