The present invention relates to a machine tool for machining of workpieces, having a workpiece support for mounting the workpiece, a tool holder, which can be moved at least along one axis, for holding a tool for machining the workpiece, and workpiece holding units for fixing the workpiece during the machining, the workpiece holding units being arranged outside the workpiece support surface of the workpiece support, which is covered by the workpiece in the mounted state, and each having a holding element for fixing the workpiece. In order that also workpieces of greater diameter can be machined, the machine tool otherwise being of the same dimensions, it is provided according to the invention that the holding elements can each be moved, substantially parallel to the workpiece support surface, in the direction of the workpiece, in particular in the direction of a central workpiece axis, which runs perpendicular to the workpiece support surface, for the purpose of centering and fixing the workpiece. The holding elements comprise a clamping surface that is arranged obliquely in relation to the workpiece support surface and that is, in the mounted state, pressed against the workpiece for fixing and centering the workpiece to be machined, thereby exerting a pressure both in the direction of the workpiece support surface and in the direction of the central workpiece axis.