The invention provides a novel process for conjugating a polymer, especially PEG, to a protein or peptide, which comprises reacting a polymeric conjugation reagent with a protein or peptide containing a polyhistidine tag under conditions such that conjugation occurs via said polyhistidine tag. The resulting conjugates are novel. The invention further relates to novel conjugates of the general formula (I) in which one of X and X&prime represents a polymer, and the other represents a hydrogen atom each Q independently represents a linking group W represents an electron-withdrawing moiety or a moiety preparable by reduction of an electron-withdrawing moiety or, if X&prime represents a polymer, X-Q-W&mdash together may represent an electron withdrawing group and in addition, if X represents a polymer, X&prime and electron withdrawing group W together with the interjacent atoms may form a ring Z represents a protein or a peptide linked to A and B via respective histidine residues A is a C1-5 alkylene or alkenylene chain and B is a bond or a C1-4 alkylene or alkenylene chain.
