Abstract: A universal head for fitting to a machine tool slide comprises a spindle head supporting a spindle and a head carrier interposed between the spindle head and the slide in order to transmit torque from the machine tool drive shaft to the spindle. The carrier is rotatable with respect to the slide and the spindle head is rotatable with respect to the carrier along mutually oblique axes. Ordinarily, relative rotation between the spindle head, carrier and machine tool are prevented by hydraulically-actuated brakes and only the spindle is driven by the drive shaft; however, when it is desired to reorient the spindle axis, rotation of the spindle is prevented while the brakes are selectively released so that drive shaft rotation results in movement of the spindle head.