The invention relates to a cosmetic process for caring for or making up keratin materials, comprising the sequential application to the keratin materials of a cosmetic composition comprising a maleic anhydride block polymer and a polyamine compound, said block polymer comprising: a first block with a glass transition temperature (Tg) of greater than or equal to 40° C. and is derived 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. and is derived from a maleic anhydride monomer and from a N 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 crosslinked polymer obtained by reacting said block polymer with said polyamine compound. 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.
