Abstract: In the obtaining of oxygen from air by low-temperature rectification in a double rectification column by compressing the air to be fractionated into higher and lower pressure partial streams; cooling said partial streams in indirect heat exchange with a nitrogen-enriched gaseous stream from the rectification column; and introducing the partial stream of the air to be fractionated which has been compressed to the higher pressure into the lower part of the high pressure column,the improvement of passing at least a part of the partial stream of the air to be fractionated which has been compressed to the lower pressure to a supplemental fractionating column operating at between the pressure ambient in the high-pressure column and the pressure ambient in the low-pressure column, withdrawing from said supplemental column a nitrogen-enriched liquid, passing the latter as reflux to the low-pressure column, engine expanding the remaining portion of the partial stream compressed to the lower pressure and/or a gaseous s