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 oxidized polysaccharide, in particular oxidized inulin, and b) at least one (poly)saccharide with amine group(s); ii) a composition comprising the ingredients a) and b); iii) the use of a) and b) 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 obtain good hair-conditioning cosmetic properties, with a long-lasting effect.