Abstract: Process for flying an aircraft in the "elevator speed maintenance mode" during altitude changes, in which for acquiring and/or maintaining a nominal speed it is supplied to the flight computer at the same time as the instantaneous speed of the aircraft, said computer producing the elevator control instruction, characterized in that a nominal speed is also simultaneously transmitted in continuous manner to the automatic thrust control member of the engines and in that the process is performed during two successive sequences, namely:a first sequence during which the elevator only receives a nose up instruction (on climbing) or a dive instruction (on descending) and the engines move to full thrust in the first case or to idling speed in the second anda second sequence, following the first, during which the real nominal speed is supplied to the elevator instruction computer and said same nominal speed increased (on climbing) or decreased (on descending) by a margin is supplied to the automatic thrust control memb