The ternary reciprocal system K+, Ba2+parallel to Br-, MoO42- has been divided into stable simplexes by a thermodynamic method, stable sections have been identified, and the heat effect of the exchange reaction at the conversion point has been calculated. We have described phase equilibria and chemical interactions in the system and located the primary crystallization fields of the phases involved. To confirm the theoretical division of the system, we experimentally studied two stable sections and three stable elements of the ternary reciprocal system K+, Ba2+parallel to Br-, MoO42- by differential thermal analysis. The experimental data demonstrate that the system is singular, irreversibly reciprocal, with eutectic melting behavior. The system is divided by stable diagonal sections into four stable phase triangles: KBr-D-2-K2MoO4, KBr-D-2-BaMoO4, KBr-D-1-BaMoO4, and BaBr2-D-1-BaMoO4 (where D-1 = 2KBr.BaBr2 and D-2 = K2MoO4 center dot BaMoO4). The division results have been confirmed by X-ray diffraction. In the stable sections, we have identified pseudobinary eutectic saddle points: e(7) (727 degrees C) and e(6) (608 degrees C). We have determined the position (melting point and composition) of three ternary eutectic points (E-1 (597 degrees C), E-2 (606 degrees C), and E-3 (602 degrees C)) and a ternary peritectic point (P1, 613 degrees C). The largest primary crystallization field in the composition square is that of barium molybdate, a refractory compound.