To provide a method which substantially produces at least either one of pure nitrogen or impure oxygen by operating a low temperature distilling column having a high pressure stage, a low pressure stage and a medium pressure stage.

A part of raw material air 10 is separated at a high pressure stage 60 and a low pressure stage 62 of a classic two-column type device and a remaining part of raw material air 10 is distilled at a medium pressure stage 24 which is operated at an intermediate pressure between the operating pressures of high and low pressure stages 60, 62. The coarse liquid oxygen 100, 110 which are discharged from the high pressure stage 60 and/or the medium pressure stage 24 have their pressure reduced and are boiled at a reboiler/condenser 106 mounted on the top of the medium pressure stage 24. The vaporized oxygen 108 discharged from the reboiler/condenser 106 is fed to the low pressure stage 62 as a vaporized material and this reduces the irreversibility of separation at the low pressure stage 62.