A shut-down procedure for an electricity delivery system comprising a fuel cell, the cell being fed with pure oxygen as oxidant and delivering an electrical voltage to an electrical power line. The electricity delivery system comprises a fuel gas circuit on the anode side, and a pure oxygen circuit on the cathode side. The shut-down procedure comprises the steps of an initial step during which the oxygen gas feed is interrupted, and an electrical consumption phase during which a hold current is drawn from the fuel cell until the pressure in the oxygen circuit reaches the water vapor pressure.