1. A compound machine tool comprising: a fixed machine block placed on a working floor; a workpiece support section arranged on said fixed machine block, and including a workpiece fitting table having a plurality of workpiece fitting surfaces that are shifted while respectively holding workpieces so as to position said workpieces at desired processing positions, and a drive source for shifting said workpiece fitting surface to said processing positions; a plurality of working sections respectively arranged around said workpiece support section on said fixed machine block, and carrying out different processes on a workpiece, said working sections including at least a machining work section and a laser beam work section, said machining work section carrying out a machining process at a machining processing position on a workpiece held on a desired workpiece fitting surface, said laser beam work section carrying out a laser beam process on the workpiece at a laser beam processing position spaced from said machining processing position; and a control means for controlling operations of said workpiece support section as well as said machining work section and said laser beam work section, so as to make it possible for the compound machine tool to successively carry out the different processes on each of different workpieces held on different workpiece fitting surfaces in a desired order.