In a process and apparatus for cutting portions such as labels or tickets from a continuously moving web, the web is passed between a blade and a co-operating support member. As the web moves past the blade, the blade is displaced during the cutting operation in the same direction as the web and synchronously therewith, but over a shorter distance than the length of the portion to be cut out. The blade is then disengaged from the web and returned to its initial starting position. The support member may also be displaced in the opposite direction to the movement of the web and blade during the cutting operation.