Process, in particular a cosmetic process, for caring for or making up keratin materials, comprising: either the topical application to the keratin materials of an anhydrous (extemporaneous) mixture of a cosmetic composition comprising a maleic anhydride acrylic polymer and of an amino alkoxysilane compound or of a cosmetic composition containing same; or the sequential application to the keratin materials of an anhydrous cosmetic composition comprising a maleic anhydride acrylic polymer and of an amino alkoxysilane compound or of an anhydrous cosmetic composition containing same, said maleic anhydride acrylic polymer being able to be obtained by polymerization of: (a) 50% to 90% by weight, relative to the total weight of monomers, of isobornyl (meth)acrylate (b) 1% to 50% by weight of maleic anhydride (c) 0 to 49% by weight of additional (meth)acrylate monomer chosen from: (i) linear or branched, saturated or unsaturated C 1 -C 20 alkyl (meth)acrylates, optionally interrupted with one or more non-adjacent heteroatoms chosen from O and S or with a group NR, R being a C 1 -C 4 alkyl group, optionally substituted with a phenyl or furfuryl group; (ii) saturated C 4 -C 8 cycloalkyl (meth)acrylates optionally interrupted with O or NH; said amino alkoxysilane having the formula: R-NH-R 1 Si(OR 2) z (R 3) x in which: R 1 is a linear or branched, saturated or unsaturated, cyclic or acyclic C 1 -C 20 hydrocarbon-based divalent group, which may be interrupted in its chain with a heteroatom (O, S, NH) or a carbonyl group, R 1 being linked to the silicon atom directly via a carbon atom; R = H or a C 1 -C 4 alkyl group, preferably H; R 2 and R 3, which may be identical or different, represent a linear or branched alkyl group comprising from 1 to 6 carbon atoms, z denotes an integer ranging from 1 to 3, and x denotes an integer ranging from 0 to 2, with z + x = 3. either the topical application to the keratin materials of an anhydrous (extemporaneous) mixture of a cosmetic composition comprising a maleic anhydride acrylic polymer and of an amino alkoxysilane compound or of a cosmetic composition containing same; or the sequential application to the keratin materials of an anhydrous cosmetic composition comprising a maleic anhydride acrylic polymer and of an amino alkoxysilane compound or of an anhydrous cosmetic composition containing same, said maleic anhydride acrylic polymer being able to be obtained by polymerization of: (a) 50% to 90% by weight, relative to the total weight of monomers, of isobornyl (meth)acrylate (b) 1% to 50% by weight of maleic anhydride (c) 0 to 49% by weight of additional (meth)acrylate monomer chosen from: (i) linear or branched, saturated or unsaturated C 1 -C 20 alkyl (meth)acrylates, optionally interrupted with one or more non-adjacent heteroatoms chosen from O and S or with a group NR, R being a C 1 -C 4 alkyl group, optionally substituted with a phenyl or furfuryl group; (ii) saturated C 4 -C 8 cycloalkyl (meth)acrylates optionally interrupted with O or NH; (a) 50% to 90% by weight, relative to the total weight of monomers, of isobornyl (meth)acrylate (b) 1% to 50% by weight of maleic anhydride (c) 0 to 49% by weight of additional (meth)acrylate monomer chosen from: (i) linear or branched, saturated or unsaturated C 1 -C 20 alkyl (meth)acrylates, optionally interrupted with one or more non-adjacent heteroatoms chosen from O and S or with a group NR, R being a C 1 -C 4 alkyl group, optionally substituted with a phenyl or furfuryl group; (ii) saturated C 4 -C 8 cycloalkyl (meth)acrylates optionally interrupted with O or NH; (i) linear or branched, saturated or unsaturated C 1 -C 20 alkyl (meth)acrylates, optionally interrupted with one or more non-adjacent heteroatoms chosen from O and S or with a group NR, R being a C 1 -C 4 alkyl group, optionally substituted with a phenyl or furfuryl group; (ii) saturated C 4 -C 8 cycloalkyl (meth)acrylates optionally interrupted with O or NH; said amino alkoxysilane having the formula: R-NH-R 1 Si(OR 2) z (R 3) x in which: R 1 is a linear or branched, saturated or unsaturated, cyclic or acyclic C 1 -C 20 hydrocarbon-based divalent group, which may be interrupted in its chain with a heteroatom (O, S, NH) or a carbonyl group, R 1 being linked to the silicon atom directly via a carbon atom; R = H or a C 1 -C 4 alkyl group, preferably H; R 2 and R 3, which may be identical or different, represent a linear or branched alkyl group comprising from 1 to 6 carbon atoms, z denotes an integer ranging from 1 to 3, and x denotes an integer ranging from 0 to 2, with z + x = 3. R 1 is a linear or branched, saturated or unsaturated, cyclic or acyclic C 1 -C 20 hydrocarbon-based divalent group, which may be interrupted in its chain with a heteroatom (O, S, NH) or a carbonyl group, R 1 being linked to the silicon atom directly via a carbon atom; R = H or a C 1 -C 4 alkyl group, preferably H; R 2 and R 3, which may be identical or different, represent a linear or branched alkyl group comprising from 1 to 6 carbon atoms, z denotes an integer ranging from 1 to 3, and x denotes an integer ranging from 0 to 2, with z + x = 3.