This invention relates to a long-arm grinding machine having an elongated shaft, one end of which is provided with a grinding head and the other end is provided with a motor. The elongated shaft is adapted to be pivotable by means of a tubular shaft bearing on a machine frame of the grinding surface width. The elongated shaft is also adapted to be slidable in the direction parallel or substantially parallel to the central position of the longitudinal axis of the elongated shaft over the griding surface length. The shaft bearing may be pivoted by means of an eccentric drive and is linked by levers to a pivotably supported ratchet support which in turn supports a ratchet lever having two oppositely constructed ratchets which can be changed over into a separate stable position at each end of the grinding surface length. The ratchets are adapted to entrain a ratchet wheel in the same of two opposite directions until a traverse has been completed in that direction, the ratchet wheel being also a component of a feed transmission whose immovable element is fixedly joined to the machine frame.