A rudder positioning unit for the steering systems of ships serves to position the rudder at an angle proportional to a rudder positioning signal received by the unit, and comprises a balance circuit having a balance signal output controlling start and stop of the steering gear of the ship, said balance circuit having inputs for the rudder positioning signal and for a feedback signal from a steering gear simulator, that is started and stopped simultaneously with the steering gear and is capable of simulating the movement of the steering gear, but at a smaller time lag than the latter or practically no time lag at all, preferably in the form of an electrical voltage. Means are provided for continuously effecting slow synchronization of the simulator with the steering gear, and for effecting quick synchronization on occurrence of a predetermined deviation between the simulator and the steering gear. A preferred form of a steering gear simulator is an electronic integrator circuit.