The invention relates to a system for detecting the angle of rotation of a rotatable element. By evaluating magnetically influenced properties of a sensor system a first magnetic field (Bext) generated or influenced by a rotating element can be detected in an evaluation circuit and used to determine the angle of rotation. By using the magnetoresistive effect over a first angular range, notable an angular range of 180°, the sensor system provides signals clearly attributable to a direction of the magnetic field (Bext). Means for applying an auxiliary magnetic field (BH) to the sensor system are provided for by means of which the signals attributable to the direction of the first magnetic field (Bext) can be modified for the definite attribution of an angle over a second angular range, notably an angular range of 360°.