For monitoring a predetermined level of a liquid in a container an ultrasonic transducer is fitted on the outer surface of the container wall at a measurement point situated at the height of the level to be monitored. The ultrasonic transducer when excited by an alternating voltage pulse having a given transmission frequency which equals the thickness resonant frequency of the container wall, transfers an ultrasonic transmission pulse to the container wall and converts ultrasonic vibrations, generated by reflected echo pulses, into electrical reception signals that are transferred to an evaluation circuit. In the evaluation circuit, on the one hand the presence or absence of echo signals is detected, and, on the other, the ultrasonic vibrations generated by the after-vibration of the container wall at the end of the transmission pulse are evaluated. As a result of this it can be determined with high error detection reliability whether the measurement point is covered by the liquid or not and whether the measurement arrangement is working satisfactorily.