The invention relates to a method for applying flat material web sections (28) to a first flat web of material (6) which is displaced in the direction of the machine having a first web speed during the production of hygiene articles or medical articles. The dimensions of the flat material web sections (28), in the direction of the machine, are smaller than the measurements of the articles which are to be produced. The flat material web sections (28) of an endless web (8) are separated in the cut-and-place method and are arranged on the first flat material web (6). The endless web (8) is fed at a second web speed to a second cutting station in the direction of a cutting roller (18). According to the inventive method, a front section (26) of the endless web (8) is applied against a surface section (24) of an anvil roller (22) which co-operates with the cutting roller (18), the surface section being curved less than the periphery (34) of the anvil roller (22). The front section (26) is cut in the endless web (8) in order to form the flat material web section (28) and each cut flat material web sections (28) is accelerated in a slip-free manner by the anvil roller (22).