A method and device for the winding up of a moving web of paper (9) on a reel spool (11), as large a part as possible of the developing wound roll (12) having a high degree of winding hardness (WH), characterized by the fact that a relatively soft intermediate layer is formed between the wound roll (12) of high winding hardness and the winding core (11). This is achieved in the manner that, during a short initial phase of the winding process, it is ensured that the winding hardness (WH) is relatively slight in the innermost layers of the wound roll (12), whereupon an immediate transition to a relatively high winding hardness (WH) is effected which is being substantially maintained during the rest of the winding-up process. Alternately, the relatively soft intermediate layer can also be created in the manner that the reel spool (11A-11D) has a soft covering (41, 42, 43, 44, 45, 46, 47) on a metal reel spool body (40).