Flying splice apparatus and method for splicing the leading end of a new web of rolled web material to a running web. The running web is trained between two coacting rotors respectively provided with coacting web press jaws. When a splice is to be made, the rotors are turned concurrently through a cycle in which the jaws coact to press the leading end of the new web against the running web. The jaw on one rotor comprises a vacuum pad to releasably hold the leading margin of the new web thereagainst. A double-faced adhesive tape is applied to the opposite margin of the new web. The jaw on the other rotor comprises an anvil and when the rotors are cycled to coact, the adhesive tape on the leading edge of the new web is pressed against the running web and the anvil jaw to adhere said leading edge to the running web and strip it from the vacuum pad, thus effectuating the splice.