A device for supplying domiciliary and ambulatory oxygen, comprising an oxygen filling station and a portable oxygen reserve that can be selectively connected to the filling station, the filling station comprising an oxygen concentrator intended to isolate gaseous oxygen from the air, a liquefier connected to one outlet of the concentrator to receive the isolated gaseous oxygen so that it can be liquefied, a transfer connector connected to one outlet of the liquefier and intended to be connected to an inlet connector of the reserve, the reserve comprising a tank connected to the inlet connector so that liquid oxygen can be transferred from the filling station to the tank, the tank comprising a gaseous oxygen outlet connected to the outlet connector via a gas heater and a flow regulating element, a delivery system comprising members for tapping off, heating and regulating the flow of the oxygen from the tank so as to deliver gaseous oxygen to a patient, the oxygen supply device comprising a gaseous oxygen outlet connector intended to be connected to the airways of a patient, the said oxygen outlet connector being situated on the portable oxygen reserve downstream of the delivery system, and an economizer capable of recirculating the boiled-off gaseous oxygen from the tank to a patient and a safety member such as a relief valve designed to release the boiled-off gaseous oxygen to the outside when the pressure within the tank exceeds a certain threshold and the economizer is not recirculating or not recirculating enough gaseous oxygen to the patient, the device having a single gaseous oxygen outlet connector intended to be connected to the airways of a patient, the said single connector being situated on the portable oxygen reserve so that the patient has to remain constantly connected to the reserve in order to be supplied with gaseous oxygen by the latter both when the reserve is connected to the filling station and when it is not.