Cosmetic detergent composition, comprises: an anionic surface-active (I) sulfate/sulfonate; an anionic carboxylic surface-active different from (I) e.g. alkyl carboxylic acid polyoxyalkylene ether with 6-24 carbon; amphoteric surface-active agent; and an ester of carboxylic acid insoluble in water e.g. esters of carboxylic acid with 3-30 carbon and alcohol of 1-30 carbon, where at least one of which is branched, in an aqueous medium. The esters are present at 0.5-10 wt.%. The ratio of anionic surface-active sulfates or sulfonate/anionic carboxylic surface-active agent is 2-12. Detergent cosmetic composition, comprises: an anionic surface-active (I) sulfate or sulfonate; an anionic surface-active carboxylic different from (I) e.g. alkyl carboxylic acid polyoxyalkylene ether with 6-24 carbon, alkylaryl carboxylic acids polyalkylene ether with 6-24 and their salts, alkylamido carboxylic polyoxyalkylene ether with 6-24 carbon and their salts; amphoteric surface-active agent; and an ester of carboxylic acid insoluble in water e.g. esters of carboxylic acid with 3-30 carbon and alcohol in 1-30 carbon, where at least one of the acid or alcohol is branched, and esters of aromatic acid with 7-30 carbon, where the carboxylic function is directly boned to the aromatic cycle and alcohol with 1-30 carbon, in an aqueous medium and the esters are present at 0.5-10 wt.%. The ratio of anionic surface-active sulfates or sulfonate/anionic carboxylic surface-active agent is 2-12. An independent claim is included for a process of washing and conditioning of the keratinous matters e.g. hair comprising applying the composition to the matters, and rinsing with water after a possible time of break.