PURPOSE: To smoothen transmission and facilitate exchange by mounting forward and reverse gears to an input shaft and an output shaft, and by providing a ball screw actuated clutch and a pair of opposite clutches between a shift collar surrounding the output shaft and the output shaft.

CONSTITUTION: A double clutch for use in a transmission 10 has a forward gear 22 and a reverse gear 23 on its input shaft 17, a forward gear 31 and a reverse gear 32 on its output shaft 25, and a play gear 33 engaging with the reverse gear 32. A large-diameter portion 35 of the output shaft 25 is provided with a ball screw actuated clutch having a ball groove 36 and a ball 37, a shift collar 38 for receiving a shift fork 44 operated by a lever, and respectively opposite friction clutches 49, 51. By selection of a screw angle of a ball screw clutch, a sufficient torque capacity is provided and only minimum force is required for a shift lever in engagement and removal.