A breathing system for an aircraft crew member or passenger may include a face-fitting device, a storage area added to a seat headrest for retaining the face-fitting device in a storage position apart from the head, and a back portion for retaining the face-fitting device on the user's head when the breathing system is used. The back portion is retained on the headrest by a removable fixing mechanism when the face-fitting device is in the storage position, and the removable fixing mechanism is released upon the tightening the face-fitting device on the user's head.