Abstract: An apparatus and method for cross-cutting a traveling web of material, such as paper, while winding the traveling web into successive rolls of a specified diameter includes a laser, a pair of spaced adhesive applicators and energy means for activating the adhesive to change it from an essentially inert to a web adhesive state. A pair of horizontally arrayed drums support a core on which the traveling web is wound. Upstream of the core, over the lower periphery of one of the drums, the on-coming web has its drum-supported surface exposed to a transversely moveable laser which cuts the web transversely to its direction of travel. Upstream of the transversely actuated laser are a pair of adhesive applicator nozzles which are spaced in the web traveling direction and movable transversely with the laser. An energy means is mounted between the adhesive nozzles and laser to activate the adhesive sprayed by the nozzles.