The process and the apparatus serve for producing pressurized gaseous nitrogen by cryogenic separation of air in a distillation column system comprising a high pressure column (4), a medium pressure column (5), a main condenser (6) and a medium pressure column top condenser (7) both in the form of condenser-evaporators. A compressed and purified feed air stream (1) is introduced into under a first pressure and cooled in the main heat exchanger (2). At least a portion (3) of the air (1) cooled in a main heat exchanger (2) is introduced into the distillation column system. A first gaseous nitrogen stream (8) from the top the high pressure column (4) is condensed in the main condenser (6). Bottom liquid (16, 19, 21, 25) of the medium pressure column (5) is evaporated and gaseous nitrogen (30) from the top the medium pressure column (5) is condensed in the medium pressure column top condenser (7). Liquid nitrogen (53) from the medium pressure column (5) is pressurized (33) to a pressure which is at least equal to the high pressure column pressure and at least partially (36) introduced into the high pressure column (4). A second gaseous nitrogen stream (40) from the top the high pressure column (4) is recovered as pressurized gaseous nitrogen product. A portion (turbine stream 43) of the compressed and purified feed air stream (1) is workexpanded in an expansion machine (42) from the first pressure to a second pressure and afterwards is warmed in the main heat exchanger (2).