The invention relates to a process for producing oxygen or air enriched with oxygen, in which process: The air entering the process is cooled in a heat exchanger to near to the condensation point of air and the air is led to a separation unit formed of two or more chambers connected thermally to each other and comprising A and B halves, in which it is divided, using liquidization and evaporation processes, into two or more gaseous fractions. The process air is maintained at normal temperature, except for small pressure differences to maintain the flow of the air and to optimize the process. When the process air flows through the A half of the separation unit, the liquid oxygen concentrate separated from it is evaporated in the B half of the separation unit at such a pressure, lower than normal pressure, that the desired composition is obtained for the oxygen concentrate and the heat of liquidization released in the A half of the unit is transferred to the B half of the unit and is bound in it to the evaporation of the oxygen concentrate. The low-oxygen-content process air leaving the A half of the separation unit is led out of the process through the heat exchanger. The oxygen concentrate evaporated in the B half of the separation unit exits at the lower than normal pressure prevailing in the half in question, either as such, or through a boosting and cooling process to the heat exchanger, and from there out of the process. The liquidization and evaporation processes are carried out in the said separation unit in nearly reversible conditions, in such a way that the gas phase in each process and in each part of the separation unit is nearly in equilibrium with the liquid phase in the same part.