A rheofluidifying surfactant composition structured into planar lamellar phases includes: a) at least one anionic surfactant and b) at least one compound selected from among amphoteric surfactants and non-ionic surfactants, in which the total active material of said surfactants is between 35 and 60% by weight relative to the total weight of said composition, in which the ratio of anionic surfactant is between 0.3 and 0.9, the ratio of amphoteric surfactant is between 0.0 and 0.7 and the ratio of non-ionic surfactant is between 0.0 and 0.7, said ratio being the ratio between the weight percentage of active material of said surfactant in said composition and the weight percentage of total active material of said surfactants in said composition, the pH of the composition being between 4 and 8, said at least one anionic surfactant being selected from the group comprising alkyl sulfates, alkyl ether sulfates, sulfonates, derivatives of phosphoric acid, phosphates and alkyl phosphates, isethionates, taurates, sulfoccinates, alkyl sulfoacetates, anionic derivatives of proteins of plant origin, amino acids and amino acid derivatives, polypeptides, carboxylic acids and the salts of same, salts of fatty acids from saponification, lactic acid derivatives and alkyl polyglucoside derivatives, and said composition being free of sodium chloride other than that which may be provided by the surfactants.