Cosmetic composition comprising: a) one or more liquid fatty substances bearing at least one hydrocarbon-based chain comprising at least 6 carbon atoms or a sequence of at least two siloxane groups; b) one or more amphoteric surfactants of formula below: R a' -C -NH-CH 2 -(CH 2) n -N (B') in which: ▪ B represents the group -CH 2 -CH 2 -O-X'; ▪ B' represents the group -(CH 2) z Y', with z = 1 or 2; ▪ X' represents the group -CH 2 -C OH, -CH 2 -C OZ', -CH 2 -CH 2 -C OH or -CH 2 -CH 2 -C OZ', or a hydrogen atom; ▪ Y' represents the group -C OH, -C OZ", -CH 2 -CH -SO 3 H or the group-CH 2 -CH -SO 3 -Z"; ▪ Z' and Z" represent, independently of each other, a cationic counterion derived from an alkali metal or alkaline-earth metal, such as sodium, an ammonium ion or an ion derived from an organic amine; ▪ R a' represents a C 10 -C 30 alkyl or alkenyl group derived from an acid R a' -C OH, which is preferably present in copra oil or in hydrolysed linseed oil, an alkyl group, especially a C 17 group and its iso form, or an unsaturated C 17 group and ▪ n represents an integer ranging from 1 to 10 and preferably from 1 to 5, ▪ or quaternized forms thereof; c) one or more thickening polymers bearing sugar units; d) one or more oxidation dye precursors and e) one or more chemical oxidizing agents, the composition comprising at least 10% by weight of liquid fatty substances, relative to the total weight of the composition. a) one or more liquid fatty substances bearing at least one hydrocarbon-based chain comprising at least 6 carbon atoms or a sequence of at least two siloxane groups; b) one or more amphoteric surfactants of formula below: R a' -C -NH-CH 2 -(CH 2) n -N (B') in which: ▪ B represents the group -CH 2 -CH 2 -O-X'; ▪ B' represents the group -(CH 2) z Y', with z = 1 or 2; ▪ X' represents the group -CH 2 -C OH, -CH 2 -C OZ', -CH 2 -CH 2 -C OH or -CH 2 -CH 2 -C OZ', or a hydrogen atom; ▪ Y' represents the group -C OH, -C OZ", -CH 2 -CH -SO 3 H or the group-CH 2 -CH -SO 3 -Z"; ▪ Z' and Z" represent, independently of each other, a cationic counterion derived from an alkali metal or alkaline-earth metal, such as sodium, an ammonium ion or an ion derived from an organic amine; ▪ R a' represents a C 10 -C 30 alkyl or alkenyl group derived from an acid R a' -C OH, which is preferably present in copra oil or in hydrolysed linseed oil, an alkyl group, especially a C 17 group and its iso form, or an unsaturated C 17 group and ▪ n represents an integer ranging from 1 to 10 and preferably from 1 to 5, ▪ or quaternized forms thereof; ▪ B represents the group -CH 2 -CH 2 -O-X'; ▪ B' represents the group -(CH 2) z Y', with z = 1 or 2; ▪ X' represents the group -CH 2 -C OH, -CH 2 -C OZ', -CH 2 -CH 2 -C OH or -CH 2 -CH 2 -C OZ', or a hydrogen atom; ▪ Y' represents the group -C OH, -C OZ", -CH 2 -CH -SO 3 H or the group-CH 2 -CH -SO 3 -Z"; ▪ Z' and Z" represent, independently of each other, a cationic counterion derived from an alkali metal or alkaline-earth metal, such as sodium, an ammonium ion or an ion derived from an organic amine; ▪ R a' represents a C 10 -C 30 alkyl or alkenyl group derived from an acid R a' -C OH, which is preferably present in copra oil or in hydrolysed linseed oil, an alkyl group, especially a C 17 group and its iso form, or an unsaturated C 17 group and ▪ n represents an integer ranging from 1 to 10 and preferably from 1 to 5, ▪ or quaternized forms thereof; c) one or more thickening polymers bearing sugar units; d) one or more oxidation dye precursors and e) one or more chemical oxidizing agents,