An apparatus (1, 1', 1") for inspection of railway axles (S1, S2) that can be installed on a railway track, the apparatus including, in association with each rail of said railway track: - at least one guide element (2E, 21), slidably engaged on which is a mobile element (4, 6) including one or more instruments (18, 20, 21, 22, 26, 28) configured for the inspection of a railway axle (S1, S2); - a motor unit (4G, 6G) configured for the displacement of a corresponding mobile element (4, 6) along said guide element (2E, 21); and - a control unit configured for the management of each motor unit (4G, 6G) and said one or more measuring instruments (18, 20, 21, 22, 26, 28), wherein said control unit is moreover configured for driving each motor unit (4G, 6G) so as to synchronize the movement of each mobile element (4, 6) with the rectilinear advancement movement of a corresponding wheel of said railway axle (S1, S2) along said track, so as to enable the inspection of the wheel in movement along the track via said one or more measuring instruments (18, 20, 21, 22, 26, 28), the apparatus (1, 1', 1") being characterized in that said motor unit (4G, 6G) includes a linear electric motor, in that it includes, for each rail of the track, a first mobile element set externally with respect to the track, wherein said first mobile element includes a first set of instruments and a second set of instruments, wherein the first set of instruments includes a first laser distance-measuring instrument and an optical-triangulation laser sensor configured for detecting a profile of a wheel of a railway axle, and wherein the second set of instruments includes: - a second laser distance-measuring instrument and an image-acquisition device configured for acquiring an image of a rolling surface of said wheel; or - the second laser distance-measuring instrument and a second optical-triangulation laser sensor mounted symmetrically with respect to said first optical-triangulation laser sensor; or - the second laser distance-measuring instrument, the second optical-triangulation laser sensor, and the image-acquisition device configured for acquiring an image of a rolling surface of said wheel, wherein moreover the image-acquisition device is preferably installed also in the first set of instruments, and in that said first and second laser distance-measuring instruments (20, 22) are arranged symmetrically with respect to a vertical centre-line axis of said first mobile element and in such a way that a measuring laser beam (L20, L22) emitted by each of them is inclined and converging with respect to said vertical centre-line axis. - at least one guide element (2E, 21), slidably engaged on which is a mobile element (4, 6) including one or more instruments (18, 20, 21, 22, 26, 28) configured for the inspection of a railway axle (S1, S2); - a motor unit (4G, 6G) configured for the displacement of a corresponding mobile element (4, 6) along said guide element (2E, 21); and - a control unit configured for the management of each motor unit (4G, 6G) and said one or more measuring instruments (18, 20, 21, 22, 26, 28), - a second laser distance-measuring instrument and an image-acquisition device configured for acquiring an image of a rolling surface of said wheel; or - the second laser distance-measuring instrument and a second optical-triangulation laser sensor mounted symmetrically with respect to said first optical-triangulation laser sensor; or - the second laser distance-measuring instrument, the second optical-triangulation laser sensor, and the image-acquisition device configured for acquiring an image of a rolling surface of said wheel, wherein moreover the image-acquisition device is preferably installed also in the first set of instruments, and