The invention pertains to an adhesive tape, more particularly for wrapping elongate material such as cable harnesses in a motor vehicle, comprising a carrier having a top side and a bottom side, the carrier, based on the cross direction, having a width BT, there being provided, on at least one long edge on the bottom side of the carrier, a strip of adhesive which has a width BK of at least 3 mm and at most 30% of the width BT, characterized in that as well as the strip of adhesive on the bottom side of the carrier, there is at least one polymer strip which extends over a width BP of at least 60%, preferably 75%, more preferably 90%, very preferably 100%, of the residual width BRB—not coated with the strip of adhesive—of the carrier.