PURPOSE: To reduce effectively power necessary for a pressure fluctuation adsorption system by controlling the system for a period in which the velocity of outflow of oxygen enriched gas or other factor during outflow is reduced.

CONSTITUTION: A compressed gaseous mixture of oxygen with nitrogen is successively fed to adsorption towers A, B, C, where nitrogen is selectively adsorbed to produce oxygen enriched gas. For example, the gaseous mixture is fed to the bottom of the tower A, and at the same time, the top of the tower A is made to communicate with the upper product outlet of the tower C from which oxygen enriched gas as a product is being released under internal pressure increased in the preceding step to equalize the pressures of the towers A, C. Nitrogen is desorbed in the tower B satd. with nitrogen. When oxygen enriched gas is released from the tower A, concd. oxygen enriched gas is fed from the top of the tower C to the top of the tower B to carry out the countercurrent cleaning of the inside of the tower B, and the gas is exhausted from the system with a vacuum pump 19. The internal pressure of the tower C is reduced. The tower A attains to a prescribed pressure by the release of oxygen enriched gas as a product. Oxygen enriched gas remaining in the upper part of the tower C is fed to the bottom of the tower B to equalize the pressures of the towers A, C. The operations are carried out in the towers A, B, C in different phases.