Abstract: The invention relates to a precision-mechanical positioning device for positioning a second component (2) relative to a first component (1) in any of the directions perpendicular to a combined straight line (3, 53) between the components. The positioning device comprises: in the first component, a basic member (5) having a first planar sliding surface (7); in the second component, a support member (6) having a second planar sliding surface (8); the support member being connected to the basic member such that the sliding surfaces bear against one another, forming a pair of sliding surfaces; the support member has holes (9) transverse to the plane of the pair of sliding surfaces, through which a locking device (4) extends to the basic member, the shanks (10) of the locking members having a thickness (D2) smaller than the hole diameters (D1); and clamping device(11) for pressing the support member into immobile contact with the basic member after the positioning has been completed.