A positioning device (59) having two transport arms (77,81) for alternately transferring plate-shaped objects from a storage position into an operational position. The transport arms are each displaceable by means of a separate manipulator (75,79), so that a quick exchange of the objects is possible. The manipulators each comprise two parallel Y-guides (83,85,97,99) which are fastened to a frame, and an X-guides (91,101) which is displaceable along the two Y-guides, while the transport arms are each displaceable along one of the X-guides. The positioning device is used in an optical lithographic device for alternately placing masks (49) on a mask support (19). A machine frame of the optical lithographic device to which the mask support is fastened is coupled to the frame of the positioning device by means of spring members.; To render an accurate positioning of the masks on the mask support possible, the optical lithographic device is provided with an optical sensor system which is coupled to an electronic control unit for controlling the positioning device.