This paper presents a theoretical study of α/α+β ternary diffusion couples. Using phase fraction-averaged fluxes, a new method is employed to treat moving α/α+β boundaries. The simulation results show that when two-phase mixtures grow, there is no concentration jump at the α/α+β boundaries. However, when two-phase mixtures dissolve, there is a composition discontinuity at the α/α+β boundaries. The current results are consistent with those in the literature where only diffusion in the matrix phase was considered.