For the eutectic composites of the LIF-RF3 (R = rare earth element, Y) system, which were prepared from the melt, the relations between (1) the electrical properties (fast fluoride ion conduction and dielectric response) of the composites and those of both corresponding single phases, (2) the composition, the preparation technique, the microstructure and the electrical properties of the composites, are examined. In the composites containing a tysonite-structured phase, the conductivity is significantly lower than that of the corresponding RF3 single crystal. A pronounced conductivity enhancement occurs in the LiF-LiGdF4 composite only. In the LiF-SmF3 composite, the significant upward jump of the conductivity is incidental to the orthorhombic --> tysonite phase transition at 496+/-5 degrees C. Simulation of the residual stress field in the fibrous LiF-TbF3 composite is performed. The influence of this field on the crack deflection is discussed.