Process and installation for the production of gaseous oxygen and/or gaseous nitrogen under pressure, of the type in which the air is distilled in a double distillation column (10) comprising a low pressure column (12) operating under a low pressure, and a medium pressure column (11) operating under a medium pressure. All the air to be distilled is compressed (in 1,4) to at least one high pressure of air substantially greater than the medium pressure, and the compressed air is cooled to an intermediate temperature. A portion of it is expanded in a turbine (5) to the medium pressure, before introducing it into the medium pressure column (11). The non-work-expanded air is liquified, then introduced after expansion (in 19, 20), into the double column; and at least one liquid product withdrawn from the double column is brought to the production pressure, and this liquid product is vaporized by heat exchange with the air. The low pressure column (12) is operated under pressure; and the residual gas from the head of the low pressure column is expanded in the second turbine (8) after having been partially reheated. The low pressure column (12) is operated under a pressure of about 1.7 to 5 bars, and the medium pressure column (11) under a pressure of about 6.5 to 16 bars.