In an electric power steering device of the type wherein an input member connected to an electric motor and an output shaft including an output member connected to a steering wheel are connected via a plurality of sets of friction clutch mechanisms for transmitting an auxiliary torque from the electric motor to the output shaft, the output member is displaceable in a radial direction relative to the input member. In response to rotation of position control members of the friction clutch mechanisms, one of the friction clutch mechanisms sets is disengaged whereupon a force or pressure exerted from the locking members of the other friction clutch mechanism sets to the output member forces the output member to move in the radial direction relative to the input member. With this movement of the output member, a frictional engagement force acting between the locking members and the input and output members is reduced. Thus, the friction clutch mechanisms can be readily disengaged by a force which is much smaller than the force required to disengage all the friction clutch mechanisms at one time.