Liquidus and solidus curves in the systems CaF2-LaF,, SrF,-LaF,, BaF,-LaF,, and MgF2-LaFJ under % atm helium pressure were determined by thermal analysis as an aid in the selection of suitable fluxes for electroslag melting of reactive metals. The systems CaF,-LaF,, SrF,-LaF,, and BaF,-LaFd 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 SrF,-LaF, and BaF,-LaF3 exhibit maxima. The system MgE-LaF, 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 a t the dystectic composition in the system SrF,-LaF,. Differences in density between metal and flux are more favorable in the system BaF,-LaF, than in pure LaF?. These observations suggest potential advantages of using fluxes from the systems studied for electroslag melting of reactive metals.