Application device for applying gripping handles on packaging films, preferably heat shrinkable, that are being supplied on shrinkwrappers for making bundles of food containers, in particular cans, tins, bottles, flasks and/or the like, the application device comprising: at least one application head provided with at least one application roller for applying a plurality of gripping handles supplied in the form of a continuous web and subsequently cut into portions, each gripping handle having adhesive ends for engagement with the corresponding packaging film, the application head comprising at least a motor or a similar actuator operatively connected to the application roller for controlling the angular velocity (w) of the latter and modifying the same according to a preset program; at least one abutment mechanism for operatively supporting a plurality of packaging films supplied in the form of a continuous web and subsequently cut into portions, the application roller of the application head and the abutment mechanism being relatively movable between a non-operating condition, in which they are not engaged, and an operating condition, in which the application roller of the application head is arranged at the abutment mechanism, against at least one of the packaging films being supplied in order to apply on the latter a respective gripping handle being supplied, the application roller of the application head being motorized and being independently controllable with respect to the feeding of the packaging films being supplied, supported by the abutment mechanism between the latter and the application roller itself, characterized in that it further comprises at least one control unit, preferably electronic and programmable, which is operatively connected to the motor or the similar actuator for rotationally actuating the application roller, the control unit modifying, for each packaging film being supplied, the angular velocity (w) of the application roller so as to determine, for at least a settable and programmable time interval, a feeding of the gripping handle being supplied that is faster than the feeding of the respective packaging film being supplied. at least one application head provided with at least one application roller for applying a plurality of gripping handles supplied in the form of a continuous web and subsequently cut into portions, each gripping handle having adhesive ends for engagement with the corresponding packaging film, the application head comprising at least a motor or a similar actuator operatively connected to the application roller for controlling the angular velocity (w) of the latter and modifying the same according to a preset program; at least one abutment mechanism for operatively supporting a plurality of packaging films supplied in the form of a continuous web and subsequently cut into portions, the application roller of the application head and the abutment mechanism being relatively movable between a non-operating condition, in which they are not engaged, and an operating condition, in which the application roller of the application head is arranged at the abutment mechanism, against at least one of the packaging films being supplied in order to apply on the latter a respective gripping handle being supplied, the application roller of the application head being motorized and being independently controllable with respect to the feeding of the packaging films being supplied, supported by the abutment mechanism between the latter and the application roller itself, characterized in that it further comprises at least one control unit, preferably electronic and programmable, which is operatively connected to the motor or the similar actuator for rotationally actuating the application roller, the control unit modifying, for each packaging film being supplied, the angular velocity (w) of the application roller so as to determine, for at least a settable and programmable time interval, a feeding of the gripping handle being supplied that is faster than the feeding of the respective packaging film being supplied.