The present invention relates to a cosmetic process for the care or makeup to keratinous materials, comprising: either the topical application on keratinous substances of an anhydrous mixture of a cosmetic composition comprising a polymer block copolymers of maleic anhydride and of an amino compound alkoxysilane or the sequential application on keratinous substances of an anhydrous cosmetic composition comprising a polymer block copolymers of maleic anhydride and of an anhydrous cosmetic composition containing an amino compound alkoxysilane, said block polymer comprising: a first sequence having a glass transition temperature (tg) greater than or equal to 40°C. from a monomer ch2 = c (r1) - coor2 with r1 = h or methyl, r2 = cycloalkyl group c4 to c12 and a second sequence having a glass transition temperature (tg) of less than or equal to 20°C. from a monomer maleic anhydride and of a monomer ch2 = c (r1) - coor3 with r1 = h or methyl, r3 = alkyl group unsubstituted in c1 to c6, linear or branched, with the exception of the tert-butyl group, or a group methoxyethyl. The present invention also relates to the polymer with alkoxysilane obtained by reaction of the block polymer with said amino alkoxysilane. The method makes it possible to obtain a deposit a film of good strength and resistance to water, oil, on the sebum, non-adhesive and not transfer.Linvention concerne un procédé cosmétique de soin ou de maquillage des matières kératiniques comprenant : soit lapplication topique sur les matières kératiniques dun mélange anhydre dune composition cosmétique comprenant un polymère séquencé danhydride maléique et dun composé amino alcoxysilane soit lapplication séquentielle sur les matières kératiniques dune composition cosmétique anhydre comprenant un polymère séquencé danhydride maléique et dune composition cosmétique anhydre contenant un composé amino alcoxysilane, ledit polymère séquencé comprenant : une première séquence ayant une température de transition vitreuse
