To obtain gaseous oxygen at a delivery pressure by providing respective processes wherein liquid oxygen is produced through the separation of air to form auxiliary refrigerant flow and the liquid oxygen is pressurized to the delivery pressure, then, the liquid oxygen is collected in the bottom unit of a mixing tower to form gaseous oxygen while the flow of liquid is evacuated to introduce the same into the middle stage of a low-pressure tower.

In order to produce liquid oxygen as the tower bottom liquid of a low-pressure tower 36 in the low-temperature rectifying process of a Claude cycle, a rectifying process, employing a high-pressure tower 28 and a low-pressure tower 36, are incorporated. Further, a Claude expander 24 expanding the half amount of air or more in the high-pressure tower 28 incorporated to form the flow of auxiliary refrigerant having a delivery pressure. The liquid oxygen is pressurized by a pump 72 from the pressure of the low-pressure tower 36 to the delivery pressure while the liquid oxygen is introduced into the top unit of a mixing tower 68 and the flow of refrigerant is introduced into the bottom unit of the mixing tower 68 to evaporate the liquid oxygen, then, the liquid is collected into the bottom unit of the mixing tower 68 to take out products from the top unit of the same tower and evacuate the liquid flow including the liquid to introduce the same into the middle stage of the low- pressure tower 36. Accordingly, gaseous oxygen product can be obtained at the delivery pressure.