We report the study of the phase diagram of a three-dimensional continuum model of symmetrical ternary amphiphilic mixtures, representing water, oil, and surfactant, using mean-held approximations as well as Monte Carlo simulations. In line with the results of various lattice models, the continuum model exhibits a region of three-(isotropic) liquid-phase coexistence consisting of water-rich, oil-rich, and surfactant-rich phases. The dependence of the phase diagram on the strength of the anisotropic water-(oil-)surfactant interactions is investigated using a modified mean-field approximation that takes into account, at the lowest level of approximation, the contribution of the water-(oil-)surfactant correlations. The phase behavior of the model ternary mixture is further examined using Monte Carlo simulation techniques in the semigrand canonical ensemble. The results of the simulations for symmetrical mixtures are consistent with the existence of a region of three-(isotropic) liquid-phase coexistence below a tricritical point. This region is analyzed in more detail using the Gibbs Monte Carlo simulation technique. It is shown that the simulation results are in qualitative agreement with the theoretical predictions. (C) 1997 American Institute of Physics.