Optical-RF double-resonance techniques have been used to study the superhyperfine transition frequencies in a series of Pr³⁺ centres in CaF₂:Pr³⁺ and SrF₂:Pr³⁺ crystals. In these centres Pr³⁺ substitutes for Ca²⁺(Sr²⁺) and the excess positive charge is compensated by F^-, H^-, D^- or T^- interstitial ions along (100) directions yielding centres of C_4v symmetry. The superhyperfine structure is associated with RF-induced nuclear spin flips of the lattice ¹⁹F^- ions and of the interstitial ions that are coupled to the Pr³⁺ ion. Some qualitative conclusions are drawn about the position of the Pr³⁺ ion, the nearest-neighbour F^- ions and the interstitial ions in the lattice.