Abstract: A ball screw device has a ball screw nut and a ball spline nut, both mounted on a shaft. Both the nuts are supported on a housing with ball bearings interposed therebetween. Inner race grooves of the ball bearings are formed on outer peripheral walls of the nuts, while outer race grooves of the ball bearings are formed on an inner peripheral wall of the housing. In another embodiment, ball insertion holes are formed through the nuts so that the ball insertion holes extend from inner peripheral walls of the nuts to the inner race grooves, respectively. The insertion holes are closed by plugs which were fitted in the insertion holes subsequent to the insertion of balls of the ball bearings through the insertion holes. In a further embodiment, a ball screw nut and a ball spline nut, both mounted on a shaft, are supported on a common housing by way of ball bearings, thereby constructing a ball screw device with a closed small space surrounded by the housing, ball screw nut, ball spline nut and shaft.