The fluorine mobility in single crystals of the anion-deficient solid solution La_1-xSr_xF_3-x (x=0, 0.001, 0.003, 0.01, 0.03, 0.05 or 0.16) with the tysonite structure has been studied in the temperature range of 130-520 K by ¹⁹F NMR. Different modes of ionic motion were identified and the leading mechanism of ionic diffusion has been suggested. The influences of temperature and fluorine vacancy concentration on the ionic mobility in tysonite have been investigated. In all crystals, fluorine diffusion begins in the F₁ sublattice. On increase in the temperature, ionic exchange between the F₁ and F_2,3 sublattices becomes observable. Addition of small amounts of Sr (x<0.003) significantly increases the ionic mobility between the sublattices. For 0.003<x<0.03 a further increase in x has no significant influence on the ionic exchange. Around x approximately=0.01 the beginning of cluster formation is noticeable. At higher concentrations (0.03<x<0.16) it is seen that ionic mobility decreases again and the guest-induced vacancies are preferentially located in the F₁ sublattice. At these doping concentrations the influence of large clusters seems to play a significant role.