The invention relates to a cosmetic process for treating keratin fibres, comprising the application to the keratin fibres of a mixture of a maleic anhydride block polymer, a liposoluble polyol and an amine catalyst； 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； and a step of heating the keratin fibres to a temperature ranging from 90°C to 250°C. The invention also relates to the crosslinked polymer obtained by reacting said block polymer with said liposoluble polyol. The treated keratin fibres have good water-resistant fixing properties.
