The electronic paramagnetic resonance of Co2+ in cubic sites of CaF2 and in trigonal sites of CdF2 have been observed at a frequency of 9 GHz and at liquid helium temperature. The trigonal spectra have an axial symmetry about a (lll) direction with g11 = 2.25 +/- 0.05 and g1 = 4.45 +/- 0.10. The origin of this trigonal center is unknown. The isotropic spectra can be described by a spin Hamiltonian with g = 2.32 +/- 0.01, u=-0.Oil +/- 0.004, A = 27.5 +/- 1.2 x lO-4 cm-1 and U = 3.5 +/- 3.5 x 10-4cm-1. The superhyperfine splitting parameters are estimated to be Af = 2.85 x 10-4cm-1 and Bf = 5.97 x lO-4cm-1. Heat treatment of the doped Ca?2 sample makes the cubic spectra diminish. This phenomenon is explained by a change in the valence' state of the paramagnetic ion. X-ray irradiation of the CaF2 sample doped with Co by diffusion changes the sample to red, but no Co^ + ions are observed. Attempts to convert the cubic spectra to trigonal ones by oxidation and hydrolysis do not yield any result.