Provided is a composition comprising, in an aqueous phase at least one anionic surfactant, at least one amphoteric and/or zwitterionic surfactant, at least one alkyl(poly)glycoside nonionic surfactant, at least on polymer chosen from cationic polymers of cationic cellulose, cationic alkyldiallylamine or dialkyldiallylammonium cyclopolymer, amphoteric polymers which comprising one or more units derived from a monomer of (meth)acrylate or (meth)acrylamide type, a monomer of (meth)acrylamidoalkyltrialkylammonium type, or a monomer of (meth)acrylic type, or a mixture thereof, and at least on fatty acid ester of glycerol and/or of polyglycerol.
