The finishing system has several finishing stations (12'-12"") which can be combined selectively to make up one finishing system (11). The workpiece holders (18) are transportable with the workpiece (17) to the individual finishing stations by a transfer system (20). The finishing stations each have a work spindle (19) which can be positioned along two axes lying in one plane and which are preferably arranged relative to each other at an angle of 90 or 45 degs. The number of work piece holders is pref. the number of finishing stations.
