The crystal structures of fully dehydrated Ni2+- and Tl+ -exchanged zeolite X (Ni17Tl58-X, and Ni12Tl68-X; X=Si100Al92O384) have been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd3 at $21(1)^{\circ}C$ (a=24.380(4) $\AA$, 24.660(4) $\AA$, respectively). Their structures have been refined to the final error indices R1=0.037 and R2=0.043 with 485 reflections, and R1=0.039 and R2=0.040 with 306 reflections, respectively, for which I >36(I). In Ni17Tl58-X, 17 Ni2+ ions per unit cell were found at only two sites: 15 at site I at the center of the hexagonal prism (Ni-O=2.203(9) $\AA)$ and the remaining 2 at site II near single six-oxygen rings in the supercage (Ni-O=2.16(3) $\AA).$ Fifty-eight Tl+ ions were found at five crystallographic sites: 28 at site II (Tl-O=2.626(8) $\AA)$, 2 at site I' in the sodalite cavity near the hexagonal prism (Tl-O=2.85(1) $\AA)$, another 2 at site II' in the sodalite cavity (Tl-O=2.77(1) $\AA).$ The remaining 26 were found at two nonequivalent Ⅲ' sites with occupancies of 23 and 3. In Ni12Tl68-X, 12 Ni2+ ions per unit cell were found at two sites: 10 at site I (Ni-O=2.37(2) $\AA)$ and the remaining 2 at site II (Ni-O=2.13(2) $\AA).$ Sixty-eight Tl+ ions were found at five crystallographic sites: 28 at site II (Tl-O=2.63(1) $\AA)$, 12 at site I' (Tl-O=2.62(1) $\AA)$, 2 at site II' (Tl-O=3.01(2) $\AA)$, and the remaining 26 at two III' sites with occupancies of 23 and 3. It appears that Ni 2+ ions prefer to occupy site I and II, in that order. The large Tl+ ions occupy the remaining sites, I', II, II' and two different III' sites. In both crystals, only the Ni2+ ions at site II were reduced and migrated to the external surface of zeolite X when these crystals were treated with hydrogen gas.