A machine for superfinishing the inner race surface of annular workpieces such as bearings with two honing stones of different grain sizes held by a common holder arm. Structure is provided for reciprocally arcuately moving the holder arm perpendicularly of the plane of rotation of the workpiece. Structure is also provided for moving the holder arm in a direction generally perpendicular to the axis of rotation of the workpiece toward and away from the inner race surface. A lever mounted on the holding arm is selectively engageable with either of the two honing stones pressing the selected honing stone toward and against the inner race surface. Structure is also provided for moving the holder arm back and forth in the direction of juxtaposition of the two honing stones a distance equal to the pitch of the two honing stones so as to alternatively position one or the other of the two honing stones for being pressed against the inner race surface by the lever, whereby the inner race surface is smoothed by one or the other of the honing stones by reciprocally moving the holder arm.
