Method for the cryogenic separation of air in a distillation column system for nitrogen/oxygen separation that comprises a first high-pressure column and a low-pressure column (25, 26) and also three condenser-evaporators, namely a high-pressure column overhead condenser, a low-pressure column bottoms evaporator and an auxiliary condenser (29; 228), in which method - a first feed air stream is cooled in a main heat exchanger (20, 21), - the cooled first feed air stream is introduced at a first pressure into the first high-pressure column, - in the high-pressure column overhead condenser, gaseous overhead nitrogen (44, 45) from the first high-pressure column is condensed, - at least one portion of the overhead nitrogen condensed in the high-pressure column overhead condenser is applied as reflux liquid to the first high-pressure column, - one portion of the bottoms liquid of the low-pressure column (25, 26) is evaporated in the low-pressure column bottoms evaporator in indirect heat exchange with a condensing heating fluid, - an unevaporated portion of the bottoms liquid of the low-pressure column (25, 26) is at least partly evaporated in the auxiliary condenser (29; 228), and - at least one portion of the liquid evaporated in the auxiliary condenser (29; 228) is obtained as a gaseous oxygen product, characterized in that - the distillation column system for nitrogen/oxygen separation further comprises a second high-pressure column, - a second feed air stream is cooled in the main heat exchanger (20, 21), - the cooled second feed air stream is passed into the second high-pressure column at a second pressure, which is higher than the first pressure, and - at least one portion of the overhead gas of the second high-pressure column is used as heating fluid in the low-pressure column bottoms evaporator. - a first feed air stream is cooled in a main heat exchanger (20, 21), - the cooled first feed air stream is introduced at a first pressure into the first high-pressure column, - in the high-pressure column overhead condenser, gaseous overhead nitrogen (44, 45) from the first high-pressure column is condensed, - at least one portion of the overhead nitrogen condensed in the high-pressure column overhead condenser is applied as reflux liquid to the first high-pressure column, - one portion of the bottoms liquid of the low-pressure column (25, 26) is evaporated in the low-pressure column bottoms evaporator in indirect heat exchange with a condensing heating fluid, - an unevaporated portion of the bottoms liquid of the low-pressure column (25, 26) is at least partly evaporated in the auxiliary condenser (29; 228), and - at least one portion of the liquid evaporated in the auxiliary condenser (29; 228) is obtained as a gaseous oxygen product, characterized in that - the distillation column system for nitrogen/oxygen separation further comprises a second high-pressure column, - a second feed air stream is cooled in the main heat exchanger (20, 21), - the cooled second feed air stream is passed into the second high-pressure column at a second pressure, which is higher than the first pressure, and - at least one portion of the overhead gas of the second high-pressure column is used as heating fluid in the low-pressure column bottoms evaporator.