A tool for the machining of workpiece surfaces, especially of drilled-hole surfaces, has at least two parts which are displaceable relative to each other. The tool for the machining of the workpiece surfaces is rotatable and includes at least one control member (19) which is displaceable relative to the tool (1) substantially perpendicularly to the axis of rotation (9) of the tool. The control member, preferably from a preset threshold speed of rotation, effects a movement of one part (5) relative to the other (3).