A steering system for vehicles or ships is provided, with a steering handwheel (11) and a steering element (1) with no mechanical linkage line therebetween, with a steering handwheel sensor device (14, 15), a steering element sensor device (16, 17) and a control arrangement (61, 62) which, in dependence on the output signals of the sensor devices (14-19), operates an electromechanical transducer (2, 3, 4, 5), on the output side of which the steering element (1) is arranged. It is desirable to increase the reliability of such a steering system. For that purpose, the control arrangement comprises at least two independent control units (61, 62), and a fault-monitoring device (28, 38) is provided which precludes a defective control unit from influencing the steering element.