Liquidus and solidus curves in the systems caf2-laf3, srf2-laf3, baf2-laf3, and mgf2-laf3 under 1/3 atmosphere helium pressure were determined by thermal analysis as an aid in the selection of suitable fluxes for electroslag melting of reactive metals. The systems caf2-laf3, srf2-laf3, and baf2-laf3 each contain (1) one eutectic, (2) no intermediate phases, and (3) two solid solutions whose lattice parameters vary linearly with composition. The liquidus curves in the systems srf2-laf3 and baf2-laf3 exhibit maxima. The system mgf2-laf3 is of the simple eutectic type with no detectable terminal solid solutions. The smallest temperature interval observed between a fluoride-flux liquidus and the melting point of ti occurs at the dystectic composition in the system srf2- laf3. Differences in density between metal and flux are more favorable in the system baf2-laf3 than in pure laf3. These observations suggest potential advantages of using fluxes from the systems studied for electroslag melting of reactive metals.