Abstract: The invention provides a method and a device for monitoring the filling of a tank with a liquid, deep-frozen gas, in which the temperature and the pressure of the liquid gas in the tank are recorded, and the mass of the liquid gas in the tank is calculated from the temperature and the volume. In the prior art, a system with an overflow was used as a filling-level limitation, in which case the height of the overflow took the maximum increase in volume into account. With this limitation of the filling level, because the phase boundary is only determined independently of the density, the maximum permissible filling level must take into account the maximum possible increase in volume of the liquid gas. With the system according to the invention, better utilization of the tank volume is possible, because the increase in volume actually possible is taken into account based on the actually prevailing pressure and temperature state of the liquid gas introduced.