Abstract: A process for concentrating or liquefying a specified component of a gaseous mixture, characterized by a combination of a step comprising passing a starting gaseous mixture containing a dilute gaseous substance to be selectively separated into one adsorbing layer of an adsorbing device consisting of a pair of adsorbing layers to allow it to adsorb the gaseous substance to be selectively separated, releasing the remainder of the gaseous mixture, and before the amount of the adsorbed gas in the adsorbing layer reaches saturation, switching the passing of the starting gaseous mixture over to the other adsorbing layer; a step comprising maintaining the pressure of the inside of the adsorbing layer which has adsorbed the gaseous substance lower than the pressure of the starting gaseous mixture fed, feeding a part of the gas released from the other adsorbing layer or an inert gas from outside the system to desorb the adsorbed gas, again passing the starting gaseous mixture after the end of desorption, and switching