Method and device for stopping of an elevator cage due to a deviation of the elevator position, acceleration, or speed from a travel curve in excess of a certain predetermined safety margin. Travel parameters, computed by the elevator control, may be passed on to a drive control of a cage drive for moving and positioning of the elevator cage, and may also be passed on to a drive control of a reference drive for moving and positioning a trigger part. Accordingly, each of the elevator cage and the trigger part may be driven by individual discrete drivers, but, due to each driver receiving the same travel parameters, the elevator cage and the trigger part move in synchronization. The trigger part may be coupled to the elevator cage to be movable when the elevator cage deviates from the computed travel curve. When the deviation from the travel curve exceeds a predetermined safety margin, the trigger part may actuate a safety switch to stop the cage or reference drivers or to arrest movement of the elevator cage.