Micellisation of the ternary mixture Tween-20, sodium deoxycholate and sodium cholate is examined in the temperature interval T = (278.15–318.15) K. Experimentally are determined: critical micelle concentration (cmc) of ternary mixtures of examined surfactants and critical micelle concentrations of binary mixtures and monocomponent surfactants. Based on the Regular solution theory, the parameters of the ternary mixed micelle are calculated from the measured cmc values. The non-ionic surfactant dominates in the amount of ternary mixed micelle. Both bile acid anions in the binary mixed micelle with Tween 20 have synergistic interactions, i.e. have negative interaction coefficients of similar magnitudes. However, sodium deoxycholate is a bile salt which, regardless of the composition of the initial ternary mixture of surfactants, represents the main amount of bile salt in the ternary mixed micelle. The entry of bile acid anions into the ternary micellar pseudophase determines which bile acid anion can reduce the total Gibbs energy of the aqueous surfactant solution, rather than their contribution to the thermodynamic stabilization of real ternary mixed micelles, relative to the hypothetical ideal state of the same micelle.