Composition for oxidatingly dyeing creatine fibre containing a thickening polymer with at least one fatty chain and a fatty alcohol with more than 20 carbon atoms

The invention relates to a composition for the oxidation dyeing of fibers keratin, in particular human keratin fibers such as the hair, comprising, in a medium appropriate for dyeing, at least one oxidation dye, at least one thickening polymer comprising at least one fatty chain and at least one fatty alcohol with more than twenty carbon atoms. The invention also relates to the dyeing processes and devices using said composition.