An intermittently operating unwinding apparatus has a splicing unit with a cross member which is movable against and at right angles to the web expiring from a winding roll. With a separating device positionable against the cross member from the other side of the web, the web is separated by lifting the empty spool mounted in the unwinding apparatus out of its unwinding position. A new parent roll whose web beginning is provided with an application of adhesive is transported by means of a conveyor to the unwinding position and the web beginning positioned relative to the splicing unit. The splicing unit holding the separated web-end at the cross member is radially moveable against the new parent roll, where the web-end meets the beginning of the web and is attached by means of the adhesive. The web length required to lead the web-end to the new roll is made ready by a dancer roller.