The invention provides reagents and methods for conjugating a polymer specifically to the .alpha.-amine of a polypeptide. The invention provides monofunctional, bifunctional, and multifunctional PEGs and related polymers having a terminal thioester moiety capable of specifically conjugating to the .alpha.-amine of a polypeptide having a cytokine or histidine residue at the N-terminus. The invention provides reactive thioester-terminated PEG polymers that have suitable reactivity with an N-terminal cysteine or histidine residue of a polypeptide to produce an amide bond between the PEG molecule and the polypeptide.