The crystal structures of fully dehydrated $Pd^{2+}$ - and $TI^{+}$ -exchanged zeolite X, $Pd_{18}TI_{56}Si_{100}Al_{92}O_{384}(Pd_{18}TI_{50-}X$, a = $24.935(4)\AA$ and $Pd_{21}TI_{50}Si_{100}Al_{92}O_{384}(Pd_{21}TI_{50-}X$ a = $24.914(4)\AA)$, have been determined by single-crystal X-ray diffraction methods in the cubic space group Fd3 at $21(1)^{\circ}C.$ The crystals were prepared using an exchange solution that had a $Pd(NH_3)_4Cl_2\;:TINO_3$ mole ratio of 50 : 1 and 200 : 1, respectively, with a total concentration of 0.05M for 4 days. After dehydration at $360^{\circ}C$ and 2 ${\times}$$10^{-6}$ Torr in flowing oxygen for 2 days, the crystals were evacuated at $21(1)^{\circ}C$ for 2 hours. They were refined to the final error indices $R_1$ = 0.045 and $R_2$ = 0.038 with 344 reflections for $Pd_{18}Tl_{56-}X$, and $R_1$ = 0.043 and $R_2$ = 0.045 with 280 reflections for $Pd_{21}Tl_{50-}X$; I > $3\sigma(I).$ In the structure of dehydrated $Pd_{18}Tl_{56-}X$, eighteen $Pd^{2+}$ ions and fourteen $TI^{+}$ ions are located at site I'. About twenty-seven $TI^{+}$ ions occupy site II recessed $1.74\AA$ into a supercage from the plane of three oxygens. The remaining fifteen $TI^{+}$ ions are distributed over two non-equivalent III' sites, with occupancies of 11 and 4, respectively. In the structure of $Pd_{21}Tl_{50-}X$, twenty $Pd^{2+}$ and ten $TI^{+}$ ions occupy site I', and one $Pd^{2+}$ ion is at site I. About twenty-three $TI^{+}$ ions occupy site II, and the remaining seventeen $TI^{+}$ ions are distributed over two different III' sites. $Pd^{2+}$ ions show a limit of exchange (ca. 39% and 46%), though their concentration of exchange was much higher than that of $TI^{+}$ ions. $Pd^{2+}$ ions tend to occupy site I', where they fit the double six-ring plane as nearly ideal trigonal planar. $TI^{+}$ ions fill the remaining I' sites, then occupy site II and two different III' sites. The two crystal structures show that approximately two and one-half I' sites per sodalite cage may be occupied by $Pd^{2+}$ ions. The remaining I' sites are occupied by $TI^{+}$ ions with Tl-O bond distance that is shorter than the sum of their ionic radii. The electrostatic repulsion between two large $TI^{+}$ ions and between $TI^{+}$ and $Pd^{2+}$ ions in the same $\beta-cage$ pushes each other to the charged six-ring planes. It causes the Tl-O bond to have some covalent character. However, $TI^{+}$ ions at site II form ionic bonds with three oxygens because the super-cage has the available space to obtain the reliable ionic bonds.