Detergent cosmetic composition (I) comprises: (a) one or more anionic surfactants comprising one or more sulfate-, sulfonate- and/or phosphate- groups in their structure (b) one or more carboxylic anionic surfactants different from the anionic surfactants (c) one or more amphoteric and/or zwitterionic surfactants (d) one or more nonionic alkyl (poly) glycoside surfactants (e) one or more cationic polymers (f) one or more zinc salts and (g) optionally one or more UV filters. Detergent cosmetic composition (I) comprises: (a) one or more anionic surfactants comprising one or more sulfate-, sulfonate- and/or phosphate- groups in their structure (b) one or more carboxylic anionic surfactants different from the anionic surfactants (c) one or more amphoteric and/or zwitterionic surfactants (d) one or more nonionic alkyl (poly) glycoside surfactants (e) one or more cationic polymers (f) one or more zinc salts and (g) optionally one or more UV filters, where the weight ratio of the amount of anionic, nonionic, amphoteric and/or zwitterionic surfactant to the amount of the zinc element or zinc salts is less than 30. An independent claim is included for coloring kit comprising a first compartment containing hair product for oxidation dyeing or direct dyeing in one or both sides, and a second compartment containing the composition.Linvention concerne une composition cosmétique détergente des fibres kératiniques, en particulier des fibres kératiniques humaines telles que les cheveux, comprenant :-au moins un tensioactif anionique (A) comprenant au moins un groupe sulfate, sulfonate et/ou phosphate,-au moins un tensioactif anionique carboxylique (B) différent du tensioactif anionique cité en (A),-au moins un tensioactif amphotère et/ou zwittérionique (C),-au moins un tensioactif non ionique alkyl(poly)glycoside (D),-au moins un polymère cationique (E),-au moins un sel de zinc (F),-et éventuellement au moins un filtre UV (G)et présentant un rapport pondéral de la quantité de tensi
