The invention relates to i) a process for treating keratin fibres, in particular human keratin fibres such as the hair, employing a) at least one monosaccharide with amine group(s), b) at least one polysaccharide with amine group(s) then c) a heat treatment; ii) a composition having an acid pH comprising the ingredients a), b) and c) at least one organic or mineral acid a), b) and c) then heat to treat keratin fibres, in particular human keratin fibres such as the hair, and iv) a multi-compartment kit or device comprising a) and b). The invention makes it possible to improve the cosmetic effect of the keratin fibres intrinsically, in order to prevent or reduce the breakage of natural keratin fibres and/or to repair damaged keratin fibres, while retaining or even improving the manageability, anti-frizz properties and/or persistence of the styling of said fibres, in particular human fibres such as the hair, when a heating step is carried out.