Abstract: A process of and apparatus for producing oxygen with a low fraction of argon from a gaseous medium like air, in which a gaseous medium is introduced into a first adsorption unit to produce an intermediate gas enriched with oxygen and depleted of argon. The intermediate gas is then supplied to a second adsorption unit in which the final product gas is prepared as well as a by-product which is returned into the process. Each of the adsorption units includes at least two adsorbers operating in a working cycle wherein the working cycle of the adsorbers of the second unit lasts about twice as long as the working cycle of the adsorbers of the first unit. For allowing an evacuation of each adsorber and thus a regeneration thereof, a common vacuum pump is connected to each unit in such a manner that the regeneration of the adsorbers of the second unit is temporarily interrupted when one of the adsorbers of the first unit is evacuated.