An adhesive-spreading unit includes a set of rollers, each of which rotates at a higher speed than the preceding one, the first roller being in contact with a tank of adhesive and the last roller sliding in contact with a film on which the adhesive is to be deposited. The unit also includes devices for distancing the rollers from one another and bring them into contact when the film has been loaded into a machine, and a single actuator unit for moving the rollers. The actuator, during the first stage of its travel, brings a rubber-clad roller into contact with the first roller, and during the second part of its travel moves the two rollers to bring the rubber-covered roller into contact with a third roller, which transfers the adhesive to the film and vice versa.