Abstract: For facilitating the rotating of a tool-receiving device, in particular an angled milling head, an elongated bushing which is concentric with respect to the milling spindle axis is secured in the milling spindle carriage. The bushing has at its free (lower) end a conical receiving opening. A support sleeve is rotatably supported in the bushing by means of radial and axial bearings. The support sleeve has at its free (lower) end a fastening flange for the tool-receiving device. Above the fastening flange is provided a centering cone conforming in shape to and fitting into the conical receiving opening. An oil film is interpositioned between the opening and the centering cone to provide a uniform support for the support sleeve. The milling spindle is supported in the support sleeve. By means of a ring gear, which is driven by a servomotor, it is possible to rotate the tool-receiving device about the axis of the milling spindle into predetermined angular positions.