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: (a) an anhydrous composition comprising at least one inert organic liquid phase and at least one sulfinic acid derivative of formula below, and also the cosmetically acceptable salts thereof: in which: R 1 is chosen from a hydrogen atom, an ion NH 3 +, a monovalent metal ion or an ionic equivalent of a divalent metal from groups la, IIa, IIb, IVa and Vlllb of the Periodic Table of the Elements; R 2 is chosen from a radical OH, a radical NR 5 R 6 in which R 5 and R 6, which may be identical or different, are chosen from a hydrogen atom and a C 1 -C 6 alkyl radical; R 3 is chosen from a hydrogen atom, an alkyl or alkenyl or cycloalkyl or aryl radical which is unsubstituted or substituted with 1 to 3 substituents, which may be identical or different, chosen from OH, C 1 -C 6, alkyl, C 1 -C 6 O-alkyl, halogen and CF 3 radicals; R 4 is chosen from a radical COOR 1, SO 3 R 1, COR 5, CONR 5 R 6 or COOR 5 in which R 1, R 5 and R 6 have the preceding meanings; R 4 also denotes a hydrogen atom when R 3 denotes an aryl radical, and in particular an aryl radical substituted as described previously; with (b) an aqueous composition with a pH of less than 5; where the inert organic liquid phase is a phase that does not lead to rapid destruction of the compounds of formula, i.e. more than 30% loss in 24 hours and that is capable of flowing at room temperature, generally between 15°C and 40°C, and at atmospheric pressure, under the action of its own weight, the pH of the mixture of the two compositions and being less than or equal to 5. (a) an anhydrous composition comprising at least one inert organic liquid phase and at least one sulfinic acid derivative of formula below, and also the cosmetically acceptable salts thereof: in which: R 1 is chosen from a hydrogen atom, an ion NH 3 +, a monovalent metal ion or an ionic equivalent of a divalent metal from groups la, IIa, IIb, IVa and Vlllb of the Periodic Table of the Elements; R 2 is chosen from a radical OH, a radical NR 5 R 6 in which R 5 and R 6, which may be identical or different, are chosen from a hydrogen atom and a C 1 -C 6 alkyl radical; R 3 is chosen from a hydrogen atom, an alkyl or alkenyl or cycloalkyl or aryl radical which is unsubstituted or substituted with 1 to 3 substituents, which may be identical or different, chosen from OH, C 1 -C 6, alkyl, C 1 -C 6 O-alkyl, halogen and CF 3 radicals; R 4 is chosen from a radical COOR 1, SO 3 R 1, COR 5, CONR 5 R 6 or COOR 5 in which R 1, R 5 and R 6 have the preceding meanings; R 4 also denotes a hydrogen atom when R 3 denotes an aryl radical, and in particular an aryl radical substituted as described previously; with R 1 is chosen from a hydrogen atom, an ion NH 3 +, a monovalent metal ion or an ionic equivalent of a divalent metal from groups la, IIa, IIb, IVa and Vlllb of the Periodic Table of the Elements; R 2 is chosen from a radical OH, a radical NR 5 R 6 in which R 5 and R 6, which may be identical or different, are chosen from a hydrogen atom and a C 1 -C 6 alkyl radical; R 3 is chosen from a hydrogen atom, an alkyl or alkenyl or cycloalkyl or aryl radical which is unsubstituted or substituted with 1 to 3 substituents, which may be identical or different, chosen from OH, C 1 -C 6, alkyl, C 1 -C 6 O-alkyl, halogen and CF 3 radicals; R 4 is chosen from a radical COOR 1, SO 3 R 1, COR 5, CONR 5 R 6 or COOR 5 in which R 1, R 5 and R 6 have the preceding meanings; R 4 also denotes a hydrogen atom when R 3 denotes an aryl radical, and in particular an aryl radical substituted as described previously; with (b) an aqueous composition with a pH of less than 5;