A method and apparatus for cutting a lead-in strip from a paper web in a multiple cylinder dryer section of a paper machine and for increasing the width of the lead-in strip by a so-called oblique draw. A cutting device for cutting the web is situated alongside a region of an unsupported draw of the web in the dryer section. According to the method, and apparatus a guide surface which extends in substantially parallel relationship to the plane of the web is associated with the web cutting device. A gas flow is directed over the guide surface to stabilize the run of the web during the cutting operation performed on the web by the cutting device. The gas flow is directed onto the guide surface from a nozzle opening situated adjacent to the leading edge region of the guide surface into a space between the guide surface and the web to produce an underpressure in the space which stabilizes the web run. Alternatively, two gas flows are directed from respective leading and trailing edge regions of the guide surface toward each other onto the guide surface into the space between the web and the guide surface to stabilize the web by means of an overpressure created in the space.