Process for cryogenic air separation in a distillation column system which has at least one single column, wherein - a compressed feed air stream (6, 8) is cooled down in a main heat exchanger in counter-current to a first recycle stream (16, 23) from the distillation column system, - the cooled feed air stream is led into the single column, - a nitrogen-rich fraction is produced in the upper region of the single column, - at least part of the nitrogen-rich fraction is condensed in a top condenser, which is constructed as a condenser-evaporator, - at least part of the liquid nitrogen-rich fraction produced in the top condenser is led into the single column as reflux, - an oxygen-containing recycle fraction is drawn off from the single column in liquid form, - the liquid recycle fraction is cooled down in a counter-current subcooler, - the cooled recycle fraction is evaporated in the top condenser, - the evaporated recycle fraction is re-compressed in a re-compressor, the re-compressor being constructed as a cold compressor, - the re-compressed recycle fraction (31, 32) is fed to the bottom of the single column, - the main heat exchanger and the counter-current subcooler are formed by an integrated heat exchanger, - the integrated heat exchanger having a first group of passages for the first recycle stream (16, 23), which goes through from the cold to the warm end of the integrated heat exchanger, - the first recycle stream (16, 23) being led into this group of passages at the cold end and flowing through the integrated heat exchanger as far as its warm end and, in the process, - being brought into indirect heat exchange both with the liquid recycle fraction and with the feed air stream, - the cooled feed air stream being drawn off from the integrated heat exchanger in completely gaseous form and being led into the single column in gaseous form, characterized in that - the first recycle stream (16, 23) is first brought into indirect heat exchange with the liquid recycle fraction in the region of the counter-current subcooler and then is brought into indirect heat exchange with the feed air stream in the region of the main heat exchanger, - the cooled feed air stream is led into the single column in completely gaseous form and - before it is fed in at the bottom of the single column, the re-compressed recycle fraction is cooled down to column temperature again in the counter-current subcoder and fed to the single column in completely gaseous form. - a compressed feed air stream (6, 8) is cooled down in a main heat exchanger in counter-current to a first recycle stream (16, 23) from the distillation column system, - the cooled feed air stream is led into the single column, - a nitrogen-rich fraction is produced in the upper region of the single column, - at least part of the nitrogen-rich fraction is condensed in a top condenser, which is constructed as a condenser-evaporator, - at least part of the liquid nitrogen-rich fraction produced in the top condenser is led into the single column as reflux, - an oxygen-containing recycle fraction is drawn off from the single column in liquid form, - the liquid recycle fraction is cooled down in a counter-current subcooler, - the cooled recycle fraction is evaporated in the top condenser, - the evaporated recycle fraction is re-compressed in a re-compressor, the re-compressor being constructed as a cold compressor, - the re-compressed recycle fraction (31, 32) is fed to the bottom of the single column, - the main heat exchanger and the counter-current subcooler are formed by an integrated heat exchanger, - the integrated heat exchanger having a first group of passages for the first recycle stream (16, 23), which goes through from the cold to the warm end of the integrated heat exchanger, - the first recycle stream (16, 23) being led into this group of passages at the cold end and flowing through the integrated heat exchanger as far as its warm end and, in the process, - being brought into indirect heat exchange both with the liquid recycle fraction and with the feed air stream, - the cooled feed air stream being drawn off from the integrated heat exchanger in completely gaseous form and being led into the single column in gaseous form, characterized in that - the first recycle stream (16, 23) is first brought into indirect heat exchange with the liquid recycle fraction in the region of the counter-current subcooler and then is brought into indirect heat exchange with the feed air stream in the region of the main heat exchanger, - the cooled feed air stream is led into the single column in completely gaseous form and - before it is fed in at the bottom of the single column, the re-compressed recycle fraction is cooled down to column temperature again in the counter-current subcoder and fed to the single column in completely gaseous form.