A system and process for monitoring the valves of an anesthetic dispenser with a safety valve (2) and with a dispensing valve (3) for dispensing the anesthetic in the form of a vapor. The valves are connected in series. A system has a downstream dispensing gap (5) and a fixed bypass resistance (9). The dispensing valve (3) is first opened for an equalization time. The safety valve (2) and the dispensing valve (3) are closed and the differential pressure between the saturated vapor branch (4) and the mixed gas branch (8) is measured by means of a differential pressure sensor (6, 7). The safety valve (2) or the dispensing valve (3) is opened and the differential pressure between the saturated vapor branch (4) and the mixed gas branch (8) is measured by means of the differential pressure sensor (6, 7). The opened safety valve (2) or the opened dispensing valve (3) is closed and the difference between the differential pressures measured are determined and compared with a preset limit value, so that the valve (2, 3) that is not opened is considered to be tight when the difference is below this limit value.