A method for monitoring the fill level of a liquid (F) in a liquid container, in particular for monitoring the coolant fill level in a reactor pressure vessel (4) of a pressurized water reactor system, wherein a determination is made about the drop in the liquid level (10) below the installed height of a heated thermal element (HT) by way of the temperature difference (DT) measured between said heated thermal element (HT) and an unheated thermal element (UHT) associated therewith, both of said elements being disposed in the liquid container, said method comprising the especially reliable triggering of an alarm with a short response time while maintaining a low level of physical and controls engineering complexity when the liquid level to be monitored falls below a critical value. To this end, according to the invention the temporal progression of the temperature difference (DT) is continuously monitored for any significant increase, in particular sudden increase, within a time interval of pre-determined duration (Delta t) prior to the respective evaluation time (t0), wherein an alarm signal is issued as soon as the change (Delta DT) in the temperature difference (DT) within said time interval reaches or exceeds a pre-determined limit value.