Abstract: The invention relates to an apparatus for controlling a machine tool during the machining of a first workpiece to be matched with a second workpiece already machined. The purpose of the invention is that of solving the problem to obtain the desired play along the entire matching section. For grinding a shaft to be matched with a bore, the apparatus comprises two pairs of measuring heads which check corresponding diameters of the shaft and of the bore, near their ends, a control unit for correcting the shape error of the shaft, preferably after a spark-out phase and before finish-grinding, and a control unit which controls the finish phase for obtaining the desired play.