Method for controlling the supply of fuel to an internal combustion engine that can be operated selectively with liquefied gas or with a fuel that is liquid at atmospheric pressure and room temperature, wherein - - the liquefied gas is delivered by means of a first low-pressure fuel pump from a first reservoir, which contains the liquefied gas, to a high-pressure fuel pump, - - the fuel that is liquid at atmospheric pressure and room temperature is delivered by means of a second low-pressure fuel pump from a second reservoir, which contains the fuel that is liquid at atmospheric pressure and room temperature, to the one high-pressure fuel pump, - - depending on the position of a switching device, the high-pressure fuel pump delivers either the liquefied gas or the fuel that is liquid at atmospheric pressure and room temperature to a high-pressure fuel accumulator which is operatively connected to individual fuel injectors (I1-I4) that are assigned to the respective cylinders (Z1-Z4) of the internal combustion engine such that, as required, either the liquefied gas or the fuel that is liquid at atmospheric pressure and room temperature is injected directly into combustion chambers of the cylinders (Z1-Z4), - characterized in that, during operation of the internal combustion engine with the liquefied gas as fuel, the fuel pressure (p R) and/or the fuel temperature (T R) in the high-pressure fuel accumulator is detected and, if predefined threshold values for the fuel pressure (p R) and/or for the fuel temperature (T R) are exceeded, a return line that connects the high-pressure fuel accumulator to the second reservoir is opened by means of an electrically actuable shut-off valve such that at least a partial stream of the liquefied gas flows, as a scavenging stream, through the high-pressure fuel accumulator back to the second reservoir. - - the liquefied gas is delivered by means of a first low-pressure fuel pump from a first reservoir, which contains the liquefied gas, to a high-pressure fuel pump, - - the fuel that is liquid at atmospheric pressure and room temperature is delivered by means of a second low-pressure fuel pump from a second reservoir, which contains the fuel that is liquid at atmospheric pressure and room temperature, to the one high-pressure fuel pump, - - depending on the position of a switching device, the high-pressure fuel pump delivers either the liquefied gas or the fuel that is liquid at atmospheric pressure and room temperature to a high-pressure fuel accumulator which is operatively connected to individual fuel injectors (I1-I4) that are assigned to the respective cylinders (Z1-Z4) of the internal combustion engine such that, as required, either the liquefied gas or the fuel that is liquid at atmospheric pressure and room temperature is injected directly into combustion chambers of the cylinders (Z1-Z4), - characterized in that, during operation of the internal combustion engine with the liquefied gas as fuel, the fuel pressure (p R) and/or the fuel temperature (T R) in the high-pressure fuel accumulator is detected and, if predefined threshold values for the fuel pressure (p R) and/or for the fuel temperature (T R) are exceeded, a return line that connects the high-pressure fuel accumulator to the second reservoir is opened by means of an electrically actuable shut-off valve such that at least a partial stream of the liquefied gas flows, as a scavenging stream, through the high-pressure fuel accumulator back to the second reservoir.