The ENDOR spectra of 55Mn2+ in KMgF3 and K2MgF4 have been measured at 4.2 °K. Whereas the spectrum in KMgF3 could be analyzed in terms of a spin Hamiltonian of cubic symmetry, the spectrum in K2MgF4 shows axial anisotropy and appropriate axial terms had to be added. The principal results are for KMgF3, Ahc=(-91. 347+/-0. 007)×10-4 cm-1; and, for K2MgF4, Dhc=(+108+/-5)×10-4 cm-1, Ahc=(-90. 809+/-0. 018)×10-4 cm-1, Bhc=(-90. 676+/-0. 014)×10-4 cm-1, and Q'h=3e2qQ40h=(+0. 19+/-0. 04) MHz. A comparison with other compounds indicates that the anisotropic part of the hyperfine structure mainly results from a second-order process, linear in the axial component of the crystalline field and linear in the dipolar hyperfine coupling. Finally, the importance of the D term for the anisotropy field in antiferromagnetic K2MnF4 is pointed out.