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 (extemporaneous) anhydrous mixture of a cosmetic composition comprising a maleic anhydride acrylic polymer and of an amino alkoxysilane compound (I)； 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 (I), wherein said maleic anhydride acrylic polymer is 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；said amino alkoxysilane having the formula (I):R—NH—R1Si(OR2)z(R3)x (I)in which:R1 is a C1-C20 hydrocarbon-based divalent group,R=H or a C1-C4 alkyl group,R2 and R3 represent an alkyl group comprising from 1 to 6 carbon atoms；z denotes an integer ranging from 1 to 3, andx denotes an integer ranging from 0 to 2,with z+x=3.Uses: skin-tensioning agent, makeup, hair fixing.
