The spin-lattice relaxation times, $T_1$, and spin-spin relaxation times, $T_2$, of the $^{27}Al$ and $^{87}Rb$ nuclei in $RbAl(CrO_4)_2{cdot}2H_2O$ crystals were investigated. The presence of only one resonance line for the $^{27}Al$ nuclei indicates that the results in a dynamical averaging of the crystal electric field that produces a cubic symmetry field. The changes in the temperature dependence of $T_1$ are related to variations in the symmetry of the octahedra of water molecules surrounding $Al^+$ and $Rb^+$. The $T_1$ values for the $^{27}Al$ and $^{87}Rb$ nuclei are different due to differences in the local environments of these ions. We also compared these $^{27}Al$ and $^{87}Rb$ NMR results with those obtained for $RbAl(CrO_4)_2{cdot}2H_2O$ crystals. The relaxation mechanisms of $RbAl(XO_4)_2{cdot}nH_2O$ (X=Cr and S) crystals are characterized by completely different NMR behaviors.