Method for the automatic shutdown of the engines of an aircraft, the aircraft comprising two engines (2, 3) and two control units (4, 5) connected to an interface device, one control unit (4, 5) being dedicated to one engine (2, 3) and being configured for activating a protection mode resulting in the shutdown of the engine when the latter is exhibiting a case of anomaly referenced in a database, a level being associated with each case of anomaly referenced in the said database, characterized in that: • below a predetermined altitude and a predetermined speed of the aircraft, following the activation of a protection mode on a first engine by a first control unit associated with the said engine, the interface device receives from the said first unit an activation signal comprising the information that a protection mode has been activated for the first engine and, on reception of the said signal, the interface device sends to the second control unit an inhibit signal comprising an instruction prohibiting the activation of a protection mode on the second engine; and • starting from a predetermined altitude and a predetermined speed of the aircraft, following the activation, by a first control unit, of a protection mode on a first engine exhibiting a case of anomaly referenced in the database, the interface device receives from the said first unit an activation signal comprising the information that a protection mode has been activated for the first engine and also receives a level signal comprising information relating to the level of the case of anomaly and, on reception of the said activation signal, the interface device sends to the second control unit an inhibit signal comprising an instruction prohibiting the activation of a protection mode on the second engine, in the case where the second engine subsequently exhibits a case of anomaly referenced in the database, the second control unit sends to the interface device a level signal comprising information relating to the level of the case of anomaly of the second engine and, on reception of the said level signal, the interface device compares the level of the case of anomaly of the first engine with that of the case of anomaly of the second engine, if the level of the case of anomaly of the second engine is the highest, the interface device sends to the second control unit an inhibit signal comprising an instruction authorizing the activation of an automatic protection mode on the second engine and the said mode is activated by the second control unit, the activation of a protection mode on the second engine remains prohibited by the interface device otherwise. • below a predetermined altitude and a predetermined speed of the aircraft, following the activation of a protection mode on a first engine by a first control unit associated with the said engine, the interface device receives from the said first unit an activation signal comprising the information that a protection mode has been activated for the first engine and, on reception of the said signal, the interface device sends to the second control unit an inhibit signal comprising an instruction prohibiting the activation of a protection mode on the second engine; and • starting from a predetermined altitude and a predetermined speed of the aircraft, following the activation, by a first control unit, of a protection mode on a first engine exhibiting a case of anomaly referenced in the database, the interface device receives from the said first unit an activation signal comprising the information that a protection mode has been activated for the first engine and also receives a level signal comprising information relating to the level of the case of anomaly and, on reception of the said activation signal, the interface device sends to the second control unit an inhibit signal comprising an instruction prohibiting the activation of a protection mode on the second engine, in the case where the second engine subsequently exhibits a case of anomaly referenced in the database, the second control unit sends to the interface device a level signal comprising information relating to the level of the case of anomaly of the second engine and, on reception of the said level signal, the interface device compares the level of the case of anomaly of the first engine with that of the case of anomaly of the second engine, if the level of the case of anomaly of the second engine is the highest, the interface device sends to the second control unit an inhibit signal comprising an instruction authorizing the activation of an automatic protection mode on the second engine and the said mode is activated by the second control unit, the activation of a protection mode on the second engine remains prohibited by the interface device otherwise.