The fluorine-ion conductivity of anion-deficient solid solutions R1−xCaxF3−x and R1−xBaxF3−x having the tysonite (LaF3) structure was investigated by the impedance spectroscopy method. R1−xCaxF3−x (R=La, Pr, Nd, Sm, Gd, Tb, Dy, Ho) and R1−xBaxF3−x (R=La, Pr, Nd) single crystals were grown from the melt by the Bridgman-Stockbarger method. The electrophysical measurements were performed in the frequency range 5−5×105 and temperature range 300–700 K. The temperature dependences of the electrical conductivity for the crystals studied is determined by the migration of fluorine anions along various structural positions. It is shown that, from the standpoint of increasing the conductivity of tysonite matrices RF3 (R=La, Pr, Nd), doping by CaF2 and BaF2 is less promising than SrF2.