The ternary reciprocal system Na+,Ba2+parallel to Br-,SO42- has been divided into simplexes by a thermodynamic method, chemical interaction in the system has been described, and its phase tree has been constructed. The melting points and compositions of the eutectic alloys in the binary system BaBr2-BaSO4 and pseudobinary system NaBr-BaSO4 have been calculated by the Schroeder method, and those of the eutectic alloys in the stable triangles NaBr-BaBr2-BaSO4 and NaBr-Na2SO4-BaSO4 of the ternary reciprocal system have been calculated by a Martynova-Susareva method. Differential thermal analysis has been used to confirm the division of the Na+,Ba2+parallel to Br-,SO42- system and experimentally study the phase compatibility triangles. We have determined the melting points and compositions of the alloys corresponding to points of invariant equilibria, described equilibrium states for each element of the ternary reciprocal system, constructed a crystallization tree, and calculated the principal thermodynamic parameters of the ternary eutectic alloys.