Abstract: A recirculating ball screw and nut mechanism wherein the screw of the mechanism comprises a shaft having an external helical groove, and the nut comprises a sleeve encircling the shaft and having an internal helical groove defining with the groove a helical working track in which run balls effective co-operation between the nut and the screw. The balls move from one end to the other of the working track during relative rotation of the nut and screw and are returned from said other end to said one end of the working track by way of a ball return path. The return path includes a groove extending around the inner wall of the sleeve and/or the outer surface of the shaft coaxial with the working track and between the convolutions of the working track without crossing the working track. The return path includes generally U-shaped regions at each for respectively diverting balls from and returning balls to the working track.