A low temperature air separation process for producing pressurized gaseous product in an air separation unit using a system of distillation columns comprises cooling a compressed air stream to a heat exchange line (30) to form a compressed cooled air stream (3), sending at least part of the compressed, cooled air stream to a column (10) of the system, liquefying a process stream to form a first liquid product, storing at least part of the first liquid product in a storage tank (50), sending at least part (60) of the above first liquid product from the storage tank to the air separation unit as one of the feeds, extracting at least one second liquid product stream (6) from a column (11) of the column system and pressurizing the at least one second liquid product stream, vaporizing the above pressurized second liquid product stream to form pressurized gaseous product in the heat exchange line and extracting a cold gas (40) without warming it completely in the heat exchange line.