An improved control system for facilitating tapping work in a machining center of the type which performs a variety of machining operations automatically. Control is effected by establishing and maintaining a certain relationship between the operation of a spindle motor which rotates a tap, and the operation of a Z-axis feed motor which transports a table longitudinally of the tap, the table mounting a workpiece. Specifically, the spindle motor and Z-axis feed motor are driven in relation to one another at all times in such a manner that the equation N.sub.s =f.sub.m /P will be satisfied, where N.sub.s (rpm) is the rotational speed of the spindle motor, f.sub.m is the feed speed of the table along the Z-axis, and P is the thread pitch of the tap. Apparatus for controlling the spindle motor includes a control circuit which is adapted to stop the spindle at a prescribed angle of rotation.