A method for shutting down an electricity supply system comprising a fuel cell, the cell being supplied with pure oxygen as the combustive gas and delivering an electric voltage to an electric power line, the system comprising a fuel gas feed circuit on the anode side and an oxygen feed circuit on the cathode side, the oxygen feed circuit comprising means that enable the said oxygen feed circuit to be opened to the atmosphere and means for delivering a stop signal to a control unit of the fuel cell. The shutting down procedure is activated on reception of a stop signal and comprises an initial stage during which the supply of oxygen is interrupted, a consumption stage during which a sustained current is drawn from the fuel cell, a neutralisation phase during which the oxygen feed circuit is opened to the atmosphere, and a final stage during which the supply of hydrogen is interrupted.