Cosmetic and conditioning detergent composition, comprises an anionic sulfate or sulfonate surface-active agent, an anionic carboxylic surface-active agent, amphoteric surface-active agent and an amino silicone, in an aqueous cosmetic medium, where the weight ratio of anionic sulfate or sulfonate surface-active agent to anionic carboxylic surface-active agent is 2-12 and the surface-active agent is present at 4-35 wt.%. An independent claim is included for a process of washing and conditioning of the keratinous matters e.g. hair, comprising application of the composition on the wet matters, and rinsing with water optionally after a pause.