An EPR study of three types of ${\mathrm{Ni}}^{+}$ centers created by x-ray irradiation of ${\mathrm{KMgF}}_{3}$:Ni single crystals is reported. The three centers have tetragonal symmetry. One of them (${\mathrm{Ni}}^{+}$-I) can be created both by 77-K and room-temperature irradiation but its EPR signal can only be observed at temperatures lower than 30 K. The other two (${\mathrm{Ni}}^{+}$-II and ${\mathrm{Ni}}^{+}$-III) are not detected in the 77-K-irradiated sample and their EPR spectra can be observed even at 300 K. The components of the g tensor of these centers are ${g}_{?}$=2.657\ifmmode\pm\else\textpm\fi{}0.002 and ${g}_{\ensuremath{\perp}}$=2.137\ifmmode\pm\else\textpm\fi{}0.005 for ${\mathrm{Ni}}^{+}$-I, ${g}_{?}$=2.578\ifmmode\pm\else\textpm\fi{}0.002 and ${g}_{\ensuremath{\perp}}$=2.108\ifmmode\pm\else\textpm\fi{}0.002 for ${\mathrm{Ni}}^{+}$-II, and ${g}_{?}$=2.545\ifmmode\pm\else\textpm\fi{}0.005 and ${g}_{\ensuremath{\perp}}$=2.085\ifmmode\pm\else\textpm\fi{}0.005 for ${\mathrm{Ni}}^{+}$-III.All these centers show a superhyperfine (shf) structure due to the interaction with four equivalent fluorine ions placed at the centers of a square perpendicular to the ${C}_{4}$ axis. The shf interaction is described by an axial tensor with ${A}_{?}$=222\ifmmode\pm\else\textpm\fi{}5 MHz and ${A}_{\ensuremath{\perp}}$=111\ifmmode\pm\else\textpm\fi{}4 MHz for ${\mathrm{Ni}}^{+}$-I, ${A}_{?}$=264\ifmmode\pm\else\textpm\fi{}4 MHz and ${A}_{\ensuremath{\perp}}$=119\ifmmode\pm\else\textpm\fi{}4 for ${\mathrm{Ni}}^{+}$-II, and ${A}_{?}$=280\ifmmode\pm\else\textpm\fi{}5 MHz and ${A}_{\ensuremath{\perp}}$=129\ifmmode\pm\else\textpm\fi{}5 MHz for ${\mathrm{Ni}}^{+}$-III. In the case of the ${\mathrm{Ni}}^{+}$-I center an extra shf structure due to the interaction with two fluorine ions symmetrically placed along the ${C}_{4}$ axis is also resolved. It is given by ${A}_{?}^{\mathcal{'}}$=15\ifmmode\pm\else\textpm\fi{}3 MHz and ${A}_{\ensuremath{\perp}}^{\mathcal{'}}$=35\ifmmode\pm\else\textpm\fi{}5 MHz. Taking into account the production, thermal stability, and behavior under optical bleaching, models for the three centers are tentatively proposed. The ${\mathrm{Ni}}^{+}$-I center is associated with a ${\mathrm{Ni}}^{+}$ ion in the center of a Jahn-Teller distorted octahedron of fluorine ions elongated along a ${C}_{4}$ axis while the ${\mathrm{Ni}}^{+}$II and ${\mathrm{Ni}}^{+}$-III defects are respectively associated with the presence of one and two nearest-neighbor fluorine vacancies along the ${C}_{4}$ axis, respectively.