A theoretical study is made of the shift of the F19 nuclear resonance in paramagnetic and antiferromagnetic MnF2 which has been observed by Shulman and Jaccarino. The problem is reduced to that of a single Mn-F pair. A net hyperfine interaction is shown to arise from overlap effects in the ground-state ionic configuration (3d)5(2s)2(2p)6 and from overlap and transfer effects to the configurations (3d)6(2s)(2p)6 and (3d)6(2s)2(2p)5. These three configurations are equivalent to a single configuration involving bonding-type molecular orbitals. The results are in reasonable agreement with the experiment, the theoretical isotropic shift being slightly too small and the theoretical anisotropic shift (small nondipolar part) being slightly too large. A re-appraisal is made of Tinkham's data on paramagnetic resonance of Mn++ impurities in ZnF2, which Bleaney has shown to be closely related to the Shulman-Jaccarino data. It is found that there is no need to include, as did Tinkham, a large fraction of fluorine 3s and 3p functions into the bond.