The invention relates to a cosmetic process for caring for or making up keratin materials, comprising: either the topical application to the keratin materials of an anhydrous mixture of a cosmetic composition comprising a maleic anhydride block polymer and of an amino alkoxysilane compound； or the sequential application to the keratin materials of an anhydrous cosmetic composition comprising a maleic anhydride block polymer and of an anhydrous cosmetic composition containing an amino alkoxysilane, said block polymer comprising: a first block with a glass transition temperature (Tg) of greater than or equal to 40° C., obtained from a monomer CH2═C(R1)—COOR2 in which R1═H or methyl, R2═C4 to C12 cycloalkyl group； and a second block with a glass transition temperature (Tg) of less than or equal to 20° C. derived from a maleic anhydride monomer and from a monomer CH2═C(R1)—COOR3 in which R1═H or methyl, R3=linear or branched C1 to C6 unsubstituted alkyl group, with the exception of a tert-butyl group, or a methoxyethyl group. The invention also relates to the polymer bearing an alkoxysilane group obtained by reacting said block polymer with said amino alkoxysilane. The process makes it possible to obtain a non-tacky and transfer-resistant film-forming deposit that has good persistence and that is resistant to water, to oil and to sebum.L'invention concerne un procédé cosmétique pour le soin ou le maquillage de substances kératiniques, comprenant : soit l'application topique, sur les substances kératiniques, d'un mélange anhydre d'une composition cosmétique comprenant un polymère séquencé d'anhydride maléique et d'un composé amino-alcoxysilane ； soit l'application, dans cet ordre, sur les substances kératiniques, d'une composition cosmétique anhydre comprenant un polymère séquencé d'anhydride maléique et d'une composition cosmétique anhydre contenant un amino-alcoxysilane, ledit polymère séquencé comprenant : une première séquence ayant une température de transition vitr
