The difficulty of pressure discontinuity in the two-fluids formulation, caused by surface tension at the interface, can now be resolved by a new concept we call ＇surface tension thickness＇. It removes one of the major barriers that the conventional two-phase flow formulation has elicited : the ill-posedness of the differential equation system. The three sets of real eigenvalues we have found at the present formulation represent such existing two-phase flow regimes as the homogeneous, slug, and separated flows. The pressure wave propagation speeds in the two-phase flows predicted by the present formulation show good agreement with the experimental data.