Micellar demixing yielding conjugate micellar phases that coexist in an aqueous solution is known for a very few surfactant systems even though the presence of two distinct types of micelles in solution has practical application. Here, on the basis of a pseudophase regular solution model for surfactant chemical potentials, we predict micellar demising to be widely prevalent in ternary surfactant mixtures that contain anionic, cationic, and nonionic surfactants. While demixing of micelles in these ternary systems has not previously been reported, the prediction is confirmed here on the basis of surface tension measurements.