A device is proposed, which makes it possible to ascertain the relative position of the reference axis BA of an object relative to a reference beam Rp of an electro-magnetic radiation, in particular a laser beam. The device displays a spatially fixed radiation transmitter S and at the object end a splitting mirror 22 as well as two position detectors 23 and 25. The splitting mirror branches a partial beam Rp′ off from the reference beam. The reference beam passing rectilinearly through the splitting mirror impinges on the one position detector and the partial beam on the other. The position detectors supply electrical signals, from which the position of the reference axis is ascertainable by means of a computer. The known devices of this species have an appreciable space requirement. This defect is eliminated by particular structuring of the beam conduction and the additional use of special optical means. Beyond that, the measurement possibilities can be enlarged through additional emission of a second reference beam Rs.