The temperature and composition dependencies of the anionic conductivity in the temperature range from ambient to 1073 K were studied for single crystals of Ca1-xGdxF2+x (x = 1 x 10(-4), 1 x 10(-3), 1 x 10(-2) and 1 x 10(-1)) and of Ca0.8R0.2F2.2 (R = La, Ce, Pr, Nd, Gd, Dy, Er, Tm, Yb, Lu and Y), having the fluorite structure. The conductivity plots for the concentrated Ca0.8R0.2F2.2 solid solutions display the low-temperature and high-temperature linear (Arrhenius) regions with the knee temperature T-k similar to 770 K. The values of the conductivity activation enthalpy obey the relation Delta H-HT(T > T-k) > Delta H-LT(T < T-k). The conductivity mechanism in heavily doped Ca1-xRxF2+x crystals is associated with the clusters of the point defects which decrease the potential barriers for fluoride anions moving by hops over the structural sites of the anion sub-lattice. We studied the effect of the dimensional factor (doped cation radii) on the anionic transport in these crystals. A correlation between anionic transport and atomic structure of the studied crystals is discussed.