The present invention relates to a method for treating at least a surface of a substrate containing labile hydrogen atoms to confer to it cytotoxic properties or cell-adhesion properties, characterized in that it comprises at least a step consisting of exposing, within a liquid medium, said substrate or a surface thereof with at least a copolymer, said copolymer containing at least a monomer unit of type A including at least a reactive site able to attach to said substrate or said surface by covalent bonds and at least a monomer unit of type B including at least one molecule able to confer antimicrobial, antiviricidal and/or antifungicidal or cell-adhesion properties to said substrate or said surface, said step being carried out in efficient conditions to promote the covalent grafting of said copolymer to said substrate or a surface thereof.