A method to automatically shutdown engines of a twin-engine aircraft where each engine is controlled by a control unit (4,5) and an interface device (6) coordinates the control units, the interface device having first and second operating modes, wherein the switching between modes is based on the airspeed and altitude of the aircraft; wherein in the first operating mode, the automatic shutdown can take place only on the first of the two engines (2,3) which exhibits an operational anomaly, and in the second operating mode, typically implemented during a cruise phase, the automatic shutdown will be able to be implemented on a first and then on a second engine (2,3) if the second engine exhibits an operational anomaly more severe than the one exhibited by the first engine.