Abstract: Apparatus for broaching a cylindrical surface of a workpiece, in which at ast one broaching tool is mounted on a tool carrier rotatable about its axis and about the axis of the cylindrical surface of the workpiece clamped in a stationary position. The broaching tool is independently rotatable about its own axis, and the rotary motion of the tool is superimposed on the rotation of the carrier and consequently the revolving motion of the broaching tool. Since the workpiece is stationary during broaching, very high cutting speeds can be achieved. The broaching tool can be of small and lightweight construction so that it is especially suitable for an automatic tool change. In a preferred form, a plurality of broaching tools are utilized, the axes of which are spaced outwardly from and circumferentially about the axis of the workpiece.