A method of managing the braking of an aircraft having landing gear with wheels fitted with friction brakes and with auxiliary brakes that enable energy to be dissipated by other than friction. The method comprises the steps of, (1) when braking is requested, testing the braking parameters to determine whether the aircraft is in a braking situation for which the friction brakes are not essential for providing the requested braking, and (2) performing the requested braking by giving priority to actuating the auxiliary brakes so long as the aircraft remains within the braking situation, and actuating the friction brakes only if the aircraft departs from the braking situation.