Abstract: A CNC automatic lathe has at least one carriage system having an X, a Y, and a Z axis that carries a tool revolver designed as a so-called disk revolver for working with lathe tools and rotary machining tools. In order to reduce as much as possible the distance between a defined cutting plane for the turning process and the carriage system, the Y axis forms with the normal to the cutting plane a relatively small acute angle (beta), so that when the tool revolver is rotated in a controlled manner around its axis, a rotatively driven machining tool mounted on the revolver and located in its working position is swivelled with its axis of rotation through an acute angle out of the cutting plane in the direction of the carriage system. The machining area of the machining tool thus described a movement with a component that extends in the minus direction of the Y axis.