Process for inerting an aircraft fuel tank, in which air enriched in inert gas is produced from a source of compressed air internal to said aircraft, and said enriched air is admitted into the tank containing the fuel, in which, during at least a cruising phase of a flight of the aircraft, there is produced a first fraction of air having a first inert gas content (T1) and this first fraction is admitted into the fuel tank (12) at a first flow rate, and, during a descent phase (34) of said flight, there is produced a second fraction of enriched air, having a second inert gas content (T2) substantially less than said first content (T1), and the second fraction and ambient air are admitted into the fuel tank at a second flow rate substantially greater than said first flow rate.