A magnetoresistive layer system including a layer sequence including at least two magnetic layers, a non-magnetic, electrically conductive intermediate layer being arranged between them; the electrical resistance of the layer system being changeable as a function of an external magnetic field acting on the layer system. At least one magnetically hard layer is integrated in the layer system, at least in certain areas, applying a magnetic field at least in the area of a boundary surface between the magnetic layers and the intermediate layer. The magnetoresistive layer system is suitable in particular for use in a GMR sensor element including coupled multilayers or in an AMR sensor element having a barberpole structure. In addition, the system includes a gradiometer including a plurality of such layer systems.