Process for treating keratin fibres with an ethylenicpolymer bearing a maleic anhydride group and a polyol 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 ethylenic polymer, a liposoluble polyol and an amine catalyst; said maleic anhydride ethylenic polymer being obtained by polymerization of: (a) 25% to 95% by weight, relative to the total weight of monomers, of an ethylenic monomer bearing an at least C8 linear or branched alkyl group; (b) 5% to 25% by weight of maleic anhydride; (c) 0% to 50% by weight of additional (meth)acrylate monomer; 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 ethylenic polymer with said liposoluble polyol. The treated keratin fibres have good water-resistant fixing properties.