A wafer-adhering adhesive tape, which has, on a surface of a base, a radiation-curable removable adhesive layer, and if necessary a die-bonding adhesive layer in order, wherein the radiation-curable removable adhesive layer is mainly composed of an acrylic-series copolymer having, in a principal chain, at least a radiation-curable carbon-carbon double bond containing group, a hydroxyl group, and a group containing a carboxyl group, respectively, and the radiation-curable removable adhesive layer has a gel fraction of 60% or greater.