The object of the present invention is a rail-mounted sliding assembly applicable to devices which are installed inside motor vehicles and which comprise moveable elements, displaceable between two rails, such as slats for concealing roofs with a transparent element or for end bars of window shades. During the sliding motion, this sliding assembly is the guided element which experiences the friction due to displacement and suppresses the play in its connection with the rail in the two coordinate directions perpendicular to the forward direction. The friction is produced in a sliding shoe and the play in one direction and the other is absorbed in independent resilient means incorporated in a supporting runner.