The rates of spin-lattice relaxation of the nuclei of ⁷Li, ²³Na, ⁷¹Ga, and ¹³⁹La ions in solutions of electrolytes are studied as functions of the concentration of a deuterated analog of solvent. An ultrahigh sensitivity of quadrupole relaxation to the symmetry of solvation sheaths of monatomic ions is shown. The data on the ion nuclei relaxation are compared to the results of investigation of the ²H and ¹⁷O nuclei of the solvent, as well as the ¹⁴N nuclei of nitrate anions. A semiquantitative description of the effects studied is given.