Apparatus for respiratory anaesthesia of a patient by administration of a gas containing gaseous xenon, with a main gas circuit which is open or closed and has an inhalation branch and an exhalation branch, means for supply of gaseous xenon to the inhalation branch of the main circuit, and means for determining the xenon concentration. The means for determining the xenon concentration comprise at least one hot-wire sensor having at least one electrically conducting wire in direct contact with the gaseous flow containing the xenon, calculating means that cooperate with the hot-wire sensor(s) in order to determine the xenon concentration (Xe %) in the flow, means for generating an electrical current in order to generate a current in at least one hot wire, and means for voltage measurement that can measure at least one voltage value at the terminal of at least one hot wire or at least one resistance arranged in series with at least one hot wire. The calculating means cooperate with the voltage measurement means in such a way as to determine the xenon concentration (Xe %).
