A device for automatically engaging an automated emergency descent of an aircraft. The device comprises a monitoring unit configured to automatically compare, repetitively, a current cabin altitude of the aircraft to an engagement threshold representing an altitude value, an activation unit configured to automatically engage the automated emergency descent when the current cabin altitude reaches the engagement threshold called main engagement threshold, and a unit for generating at least one engagement threshold configured at least to adapt the main engagement threshold according to the terrain, the main engagement threshold corresponding to the sum of a terrain altitude and a predetermined margin.