in which Pr represents said protein or peptide, each Nu represents a nucleophile present in or attached to the protein or peptide, each of A and B independently represents a C1-4alkylene or alkenylene chain, and W′ represents an electron withdrawing group or a group obtained by reduction of an electron withdrawing group; and in which said polyethylene glycol portion is or includes a pendant polyethylene glycol chain which has a terminal end group of formula —CH2CH2OR in which R represents a hydrogen atom, an alkyl group, or an optionally substituted aryl group. Also claimed are a method for making such a conjugate, and novel reagents useful in that method.