The impedance spectra of oriented single crystals of LaF3 and CeF3 doped with SrF2 (0-16 atom%) were measured for different directions of charge transport in the temperature range 290-770 K. At lower temperatures (T < 420 K), charge transport parallel to the crystallographic c-axis is accompanied by an additional time constant in the impedance spectra and can be represented in the equivalent circuit by an additional resistance and capacitance. This feature vanishes completely at temperatures higher than 420 K. It was not observed for charge transport perpendicular to the c-axis. The results are evaluated based-on an impedance model of Franceschetti and Shipe. The fluoride ion conductivity sigma(F-) along the c-axis is about a factor of two higher than in a perpendicular direction. The capacitance for transport in c-direction is due to a charge storage effect on trapping F2/F3 sites with longer life times. The anisotropy results from different jump frequencies between the three non-equivalent types of F- sites and their different contribution along the c-axis and perpendicular to that direction.