Process and apparatus for winding a running material web, in particular a paper or cardboard web, in which the running material web is wound consecutively on several winding cores, in particular reel spools. At least one cut is made preferably running parallel to the web edge of the running material web and in the web travel direction of the running material web. After the started at least one cut has run through the nip formed by the winding roll and the new winding core, the at least one formed transfer strip which is incorporated in the running material web is detached from the outer circumferential area of the winding roll by at least one directed high-energy air jet that is generated briefly by at least one separator device and simultaneously cuts through. Subsequently, the at least one now detached transfer strip is transferred onto, and preferably applied to, the outer circumferential area of the new winding core by at least one first blower device, in particular a blower shoe.