The hyperfine interactions of the
F
centre electron (an electron trapped at an anion vacancy) with the four nearest fluorine shells have been measured by the endor method in CaF
2
, SrF
2
and BaF
2
. The third shell fluorines are divided into two separate groups, labelled 3
a
and 3
b
, which are characterized by the presence and absence of a cation between the
F
centre and the fluorine. The hyperfine interaction with 3
a
fluorines shows the unusual feature of increasing form CaF
2
to BaF
2
; all other shells show a decrease. In the case of the
F
centre with the magnetic Ba nuclei in the nearest Ba shell has also been measured by the endor method. The hyperfine constants of the
F
centre in CaF
2
, SrF
2
and BaF
2
have been calculated and are compared with experiment. The theoretical wavefunctions used are the sum of a spherically symmetric part and anisotropic parts. The wavefunctions are orthogonalized to the other occupied orbitals in the crystal. The isotropic parts are taken from Bennett & Lidiard's point-ion calculation and give reasonable agreement with experiment. The anisotropic terms are needed because the
F
centre has only tetrahedral symmetry. The admixture of these terms is calculated by perturbation theory using the point ion model and anisotropic function from a continuum calculation. It is possible to get reasonable agreement with the anisotropy in the hyperfine constants found experimentally. The discrepancies are analysed as a preliminary to more sophisticated colour centre calculations.