In a toroidal stepless transmission having a forward-backward drive change over mechanism between an input shaft and an input disk, an actuator which controls the inclination angles of power roller is controlled by separate controllers according to the drive direction of the vehicle. In order to change over between these two controllers, a spool is provided which displaces in an axial direction between a forward drive position and a backward drive position according to the rotation direction of an output disk. A transfer shaft which rotates in synchronism with the output disk and transfers the output torque to drive shaft of the vehicle, is also used for displacing the spool. A drive gear is fixed to this transfer shaft, and a driven gear to which a rotation force due to engagement with the drive gear and a sliding frictional force in an axial direction are transmitted, is fitted over the spool. Due to the rotation of the drive gear, the driven gear rotates around the spool and simultaneously drives the spool between the forward drive position and the backward drive position due to the sliding frictional force, depending on the rotation direction of the output disk.