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, a medium pressure column, a main condenser and a medium pressure column top condenser. A compressed and purified feed air stream is introduced into under a first pressure and cooled in the main heat exchanger. At least a portion of the air cooled in a main heat exchanger is introduced into the distillation column system. A first gaseous nitrogen stream from the top the high pressure column is condensed in the main condenser. Bottom liquid of the medium pressure column is evaporated and gaseous nitrogen from the top the medium pressure column is condensed in the medium pressure column top condenser. Liquid nitrogen from the medium pressure column is pressurized to a pressure which is at least equal to the high pressure column pressure and at least partially introduced into the high pressure column. A second gaseous nitrogen stream from the top the high pressure column is recovered as pressurized gaseous nitrogen product. A portion (turbine stream) of the compressed and purified feed air stream is expanded in an expansion machine from the first pressure to a second pressure and afterwards is warmed in the main heat exchanger.