Process for generating a liquid oxygen product and a gaseous oxygen product by low-temperature separation of air in a distillation column system of an air separation facility which has a high-pressure separation column and a low-pressure separation column with which, in order to obtain the liquid oxygen product, a liquid fraction having a first, higher oxygen content is extracted from the low-pressure separation column of the distillation column system and is discharged in liquid form from the air separation facility and with which, in order to obtain the gaseous oxygen product, a liquid fraction having a second, lower oxygen content is extracted from the same low-pressure separation column of the distillation column system, is evaporated in a mixing column against mixing column air, is heated in a main heat exchanger against feed air to be cooled and is then discharged in gaseous form out of the air separation facility, wherein - the low-pressure separation column comprises a single condenser for generating rising gas in the low-pressure separation column, - a first partial flow of the total air is expanded to perform work in a first expansion machine to the operating pressure of the high-pressure separation column, and is fed into the high-pressure separation column, - a second partial flow of the total air is used as the mixed column air in that - the second partial flow of the total air is expanded to perform work in a second expansion machine to the mixing column pressure and fed into the mixing column in a lower region, - the two expansion machines have different inlet temperatures - one (X1; X2) of the two expansion machines is coupled to a booster in which the air flow, which is then introduced into the expansion machine coupled to the booster, is previously compressed, - the other (X2; X1) of the two expansion machines is mechanically coupled to a generator and/or an oil brake, - either the first partial flow or the mixing column air is cooled in indirect heat exchange with a nitrogen-rich fraction (r) from the low-pressure separation column downstream of the work-performing expansion (X1; X2) in the main heat exchanger, - the sump of the low-pressure separation column and the head of the high-pressure separation column are thermally coupled to each other via the condenser, - the low-pressure separating column and the high-pressure separating column have only one such condenser, and - the liquid fraction having the first oxygen content is extracted from the sump of the low-pressure separation column, and the liquid fraction having the second oxygen content is extracted from the low-pressure separation column at a different height. - the low-pressure separation column comprises a single condenser for generating rising gas in the low-pressure separation column, - a first partial flow of the total air is expanded to perform work in a first expansion machine to the operating pressure of the high-pressure separation column, and is fed into the high-pressure separation column, - a second partial flow of the total air is used as the mixed column air in that - the second partial flow of the total air is expanded to perform work in a second expansion machine to the mixing column pressure and fed into the mixing column in a lower region, - the two expansion machines have different inlet temperatures - one (X1; X2) of the two expansion machines is coupled to a booster in which the air flow, which is then introduced into the expansion machine coupled to the booster, is previously compressed, - the other (X2; X1) of the two expansion machines is mechanically coupled to a generator and/or an oil brake, - either the first partial flow or the mixing column air is cooled in indirect heat exchange with a nitrogen-rich fraction (r) from the low-pressure separation column downstream of the work-performing expansion (X1; X2) in the main heat exchanger, - the sump of the low-pressure separation column and the head of the high-pressure separation column are thermally coupled to each other via the condenser, - the low-pressure separating column and the high-pressure separating column have only one such condenser, and - the liquid fraction having the first oxygen content is extracted from the sump of the low-pressure separation column, and the liquid fraction having the second oxygen content is extracted from the low-pressure separation column at a different height.