The present invention relates to a process for stripping keratin fibres, and in particular human keratin fibres such as the hair, dyed with oxidation dyes and/or direct dyes, using a composition obtained by extemporaneous mixing of an anhydrous or aqueous composition (A) comprising at least one suitably selected sulfinic acid derivative and an aqueous composition (B) with a pH of less than (5), comprising at least one organic acid other than the compounds of formula (I), with a pKa of less than or equal to (4) when the composition (A) is aqueous, the pH of the mixture of the two compositions (A) and (B) being less than or equal to (5). The invention also relates to a composition for stripping the artificial colour from keratin fibres, comprising at least one suitably selected sulfinic acid derivative and at least one thickener chosen from anionic polymers and nonionic polymers. The compositions used in the context of the invention afford efficient stripping, especially in terms of power, of the artificial colour of keratin fibres dyed with a wide range of oxidation dyes and/or direct dyes. They do not induce lightening of the natural base of the keratin fibres and limit the sensitization of the keratin fibres. They apply well to the hair, uniformly, which makes it possible to obtain regular stripping of the colour along the entire fibre.
