A processing method for automatically opening a slide-open package of tobacco articles with a hinged lid; the package comprising: an inner container housing a group of tobacco articles and having an open top end; an outer container housing the inner container to allow the inner container to slide with respect to the outer container between a closed configuration, in which the inner container is inserted inside the outer container, and an open configuration, in which the inner container is partly expelled from the outer container; and a hinged lid which, when closed, closes the open top end of the inner container; the processing method comprising the steps of: mechanically clamping the outer container; and exerting pull on the lid to rotate the lid into an open position by means of a first actuator, which contacts a top wall of the lid, and has a first suction head which engages the top wall by suction; the processing method being characterized by comprising the further step, simultaneous and coordinated with the step of exerting pull on the lid, of exerting thrust on the inner container, to slide the inner container axially with respect to the outer container, by means of a second actuator, which contacts a wall (7; 9) of the inner container through a window formed through a corresponding wall (14; 16) of the outer container. an inner container housing a group of tobacco articles and having an open top end; an outer container housing the inner container to allow the inner container to slide with respect to the outer container between a closed configuration, in which the inner container is inserted inside the outer container, and an open configuration, in which the inner container is partly expelled from the outer container; and a hinged lid which, when closed, closes the open top end of the inner container; the processing method comprising the steps of: mechanically clamping the outer container; and exerting pull on the lid to rotate the lid into an open position by means of a first actuator, which contacts a top wall of the lid, and has a first suction head which engages the top wall by suction; the processing method being characterized by comprising the further step, simultaneous and coordinated with the step of exerting pull on the lid, of exerting thrust on the inner container, to slide the inner container axially with respect to the outer container, by means of a second actuator, which contacts a wall (7; 9) of the inner container through a window formed through a corresponding wall (14; 16) of the outer container. mechanically clamping the outer container; and exerting pull on the lid to rotate the lid into an open position by means of a first actuator, which contacts a top wall of the lid, and has a first suction head which engages the top wall by suction; the processing method being characterized by comprising the further step, simultaneous and coordinated with the step of exerting pull on the lid, of exerting thrust on the inner container, to slide the inner container axially with respect to the outer container, by means of a second actuator, which contacts a wall (7; 9) of the inner container through a window formed through a corresponding wall (14; 16) of the outer container.