In the radially adjustable tool head there is provided a radially adjustable slide serving to accommodate a cutting tool. The slide is arranged to slide on a spindle insert at guiding members containing guiding or guide surfaces which slide in pairs upon each other. To positively retain the slide on the spindle insert springs are arranged in such a manner and with a pre-bias such that the guiding surfaces are pressed against each other. Also, structure is provided to interrupt, when desired, the transmission of the pre-bias to the guiding surfaces.