In a numerical-control machine tool use is made of a mandrel-holding structure that makes it possible for the machine tool to be used to smoothing/facing and polishing purposes under utilization of traditional pan-like tools, in which the force acting on the working tool is delivered by a pre-established adjustable pneumatic pressure, while the weight of the moving parts of the mandrel is compensated for by a compression spring. When the pneumatic pressure is substituted for by an oleodynamic, i.e. oil-pressure force acting in the opposite direction, the machine switches over to normal operating conditions as a regular numerical-control machine tool.