PURPOSE: To relieve interference between a cage and an engaging element at the load time of torque in a two-way differential clutch for tilting the engaging element by the relative rotation of two cages between track members.

CONSTITUTION: A pin 19 protruding from an outer ring 1 is fitted into an oblong groove 18 provided at an outer cage 6, and the pin 19 is positioned to the center of the oblong groove 18 by elastic members 22, 23. When interference is about to be generated between a sprag 11 and the outer cage 6 at the load time of torque, the elastic members 22, 23 are deformed, and the outer cage 6 is rotated relatively to the outer ring 1 so as to relieve the interference. Upon the release of torque load, the outer cage 6 is returned into the original position by the energizing force of the elastic members 22, 23.