New fast F- ion conductors with tysonite-type structure have been obtained inside anion-deficient non-stoichiometric solid solutions of Ln(1-y)Cd(y)F(3-y) formulation (Ln = Ce, Nd). An exchange mechanism between fluoride sublattices has been identified for the (y not equal 0) compositions. A second exchange mechanism at lower temperature has been shown for CeF3 and NdF3. The presence of both electrical anomalies in the temperature dependence of LnF(3) (Ln = Ce, Nd) is confirmed by C-p variation and X-ray diffraction analysis as a function of temperature.