The first EPR measurements of the hyperfine structure of tetragonal centres of U 5+ in NaF and LiF are reported. These spectra (observed at 77K) are characterized by a very large electric quadrupole splitting larger or of the same order of magnitude as the magnetic hyperfine interaction. An analytical method has been developed for evaluating the hyperfine and quadrupole coupling parameters. Exact numerical diagonalization was required for the best fitting.