The invention relates to a device for the oxygen-enrichment of respiratory air, which comprises an inlet (21) for compressed ambient air to which a compressor for providing compressed ambient air can be connected, a cooling dryer (4) for dehumidifying said compressed ambient air, and a separator device (20), said separator device (20) being provided with an inlet (13a) for the compressed and dehumidified ambient air, a first outlet (13b) that is directly connected to said inlet, and a second outlet (13c) that is connected to the inlet (13a) by means of a selective membrane (13). The permeability of the selective membrane (13) is, under predetermined conditions, higher for oxygen than it is for nitrogen. A heating device (11) for heating up the compressed and dehumidified ambient air is provided in the flow path between the cooling dryer (4) and the inlet (13a) of the separator device (20).
