The present invention provides a complex machine tool wherein the punching center is coincides with the cutting work position so that the range of movement of a workpiece is not subjected to any restriction even during the workpiece cutting work in the same manner as in the workpiece punching work. The composite machine tool comprises a plasma torch (16) mounted on the machine tool body near the working position and arranged to be movable freely such that it can be withdrawn from the working position when a workpiece (5) is subjected to die-punching work, and proceeded to the working position when the workpiece is subjected to cutting work. Futher, the machine tool comprises protecting means (18, 19) for protecting the lower turret (3) and other members mounted adjacent thereto from the dross and heat developed by plasma arc during the workpiece cutting work by the plasma torch.