A biocompatibilizing process in which a substrate having a surface which bears substrate pendant functional groups is biocompatibilized by coating it with a coating composition containing a polymer formed from a radical polymerizable monomers including a radical polymerisable zwitterionic monomer and a radical polymerizable monomer containing a reactive group to form a polymer having zwitterionic groups and pendant reactive groups and the said pendant reactive groups are reacted to form covalent bonds with said substrate pendant functional group and thereby form a stable coating of polymer on the said surface.