The ionic conductivity of single crystals of tysonite-type solid solutions Lal_xBaxFa_x(O • x • 0.095) has been studied parallel and perpendicular to the crystallographic c axis in the temperature range 293-1300 K. Three regions can be discerned in the compositional dependence of the ionic conductivity: (i) the "pure" crystal, in which at room temperature no exchange occurs between different types of anion sites in the tysonite structure; (ii) an intermediate region (0 < x < 7 X 10 -2) which reveals changes in both the conductivity activation enthalpy and the magnitude of the conductivity; (iii) a concentrated solid-solution region (x > 7 X 10-2), where fluoride ions interchange easily among the different anion sublattices. Diffusion coefficients calculated from ionic conductivity results, are in good agreement with those calculated from 19F NMR measurements. Using the present data, along with 19F NMR data, dielectric relaxation data and structural considerations, mechanisms governing the ionic conductivity are proposed.