Abstract: A process for insertion of an accurately positioned second core tube provided along a generatrix with means for adhering the head end of a web into the wedge formed by two rotatable support rolls of a winding machine, and for ejection of a first tube supported by said support rolls and wound with said web comprising ejecting the first wound tube from the wedge to a position where it no longer contacts both support rolls, while ejecting the first tube displacing a second tube carrying means for adhesion to the web to a position adjacent said wedge, severing the web when the first tube reaches inoperative position, and discharging the second tube into the wedge so as to be rotated by the support rolls, the adhesion means on the second tube causing it to adhere the severed web thereto for winding on the rotating second roll.