Apparatus for causing paper webs to tear off within rewinding machines, the web (2) being provided, at regular intervals, with transverse perforation which subdivide the web into sheets joined to each other but able to be separated in correspondence of said perforation lines, the apparatus comprising a device to cause the tearing of the web (2) upon the passage of a perforation line (p) which separates the last sheet of a log (RO) in the course of formation from the first sheet of the next log to be formed, characterized in that the tearing device is a pneumatic type device (SP) able to direct a jet of compressed air toward the line (p).