A motion sensor which has a coil that surrounds a ferromagnetic core and at least one magnet that is longitudinally movable along the coil. The magnet causes a magnetic saturation of the ferromagnetic core in an associated zone that covers a portion of the length of the coil. An evaluation unit generates a position signal in dependence on the position of the movable magnet along the longitudinal extent of the coil. The coil has at least two superimposed winding layers that surround the ferromagnetic core and are wound in opposite directions. The windings of adjacent segments generally have about the same width over which the winding density remains constant. Thus, the winding density of the segments of one of the winding layers increases linearly over the length of the sensor while the winding density of the segments in the other winding layer linearly decreases over the sensor length.