A fuel level sensors eliminates lines to the sensor through the container wall. The novel level transmitter has a sensor made from magnetostrictive material which is stimulated to oscillate by an alternating magnetic field from a transceiver unit. These oscillations are detected by the transceiver unit, fed to an evaluation unit and used to form a signal for the level. The level transmitter and the method are particularly suitable in the case of use in fuel containers of motor vehicles.