The invention relates to a travelling device (1) for milling rail heads (2) of rails (4) arranged in a bed (3), having a rotatably driven cutter head (5) that is mounted in a travelling mechanism (6) bearing a cutter head drive (7), wherein the cutter head (5) has at least one cutting tooth composed of a plurality of cutting edges for milling the rail heads (2). According to the invention provision is made for the cutter head (5) to have a disc-shaped tool carrier (14) having peripherally arranged cassettes (16) tipped with cutting edges (31), which cassettes are arranged on a plurality of carrier segments (15) releasably connected to the tool carrier (14), wherein the tool carrier (14) is connected to the cutter head drive (7) and/or are arranged on the peripherally at least two cassettes (16) that are tipped with cutting edges and differ from one another in respect of the number of cutting teeth and/or the distances of the cutting teeth from one another and/or the effective cutting angle of the individual c
