For producing a pressurized product by low-temperature producing a pressurized product by low-temperature fractionation of air in a rectification system which has a high-pressure column (13) and a low-pressure column (14), a first feed airstream (12) is introduced into the high-pressure column (13), and an oxygen-rich fraction (38) from the low-pressure column (14) is brought (39) to pressure in the liquid state and introduced (41) into a mixing column (16). A second feed airstream (6, 15) is introduced into the lower region of the mixing column (16) and brought into countercurrent contact with the oxygen-rich fraction (41). The mixing column (16) is operated at a pressure (PM1S) which is lower than the operating pressure (pHDS) of the high-pressure column (13). A total airstream (1) which comprises the first and second feed airstreams is compressed (2) to a first pressure (p1) which is lower than the operating pressure (pHDS) of the high-pressure column (13) and is purified (3) at about this first pressure (p2) . The purified total airstream (4) is divided into the first (5) and the second (6) feed airstream. The first feed airstream (5) is further compressed (8) separately from the second feed airstream to a second pressure (P2) which is at least equal to the operating pressure (PHDS) of the high-pressure column (13).