Methods are provided for the preparation of conjugates of a variety of bioactive components, especially proteins, with water-soluble polymers (e.g., poly(ethylene glycol) and derivatives thereof), which conjugates have reduced antigenicity and immunogenicity compared to similar conjugates prepared using poly(ethylene glycol) containing a methoxyl or another alkoxyl group. The invention also provides conjugates prepared by such methods, compositions comprising such conjugates, kits containing such conjugates or compositions and methods of use of the conjugates and compositions in diagnostic and therapeutic protocols.