Temperature dependent NMR measurements as well as XAS investigations on La_1-xSr_xF_3-x (x=0.0, 0.01, 0.05, 0.16) have been performed to study the fluorine diffusion in these solid electrolytes and to elucidate the effect that doping with heterovalent SrF₂ has on LaF₃. A three-stage process of diffusion was observed. Upon increasing temperature, initial ionic exchange begins in the F₁ sublattice. At even higher temperatures, dependent upon dopant concentration, ionic exchange between the F₁ and F_2,3 sublattices takes place. A further increase in temperature eventually leads to exchange over all F^- structural positions.