A rotary driving apparatus including internally-meshing planetary reduction gear to which the output rotation of a motor is inputted, a drive shaft to which the output rotation of the planetary reduction gear is transmitted, an output rotary shaft to which the rotation of the drive shaft is transmitted, and a rotary flange provided on the output rotary shaft with a wheel mounted on the flange. The speed of the output rotation of the motor is reduced and then transmitted to the wheel so as to cause a vehicle to run on the wheel. The apparatus further includes a free-wheel mechanism comprising first axially-slidable engagement means provided between the drive shaft and an external gear of the planetary reduction gear, second axially-slidable engagement means provided between the drive shaft and the output rotary shaft, an operational shaft which is arranged to be fixed to an end portion of the drive shaft and which is slidable axially and capable of being fixed at an axial position, a guide in which the operational shaft is guided, and means for permitting the operational shaft to slide axially. When the operational shaft is slid axially, at least the engagement between the drive shaft and the external gear is either established or interrupted.