A combined theoretical and experimental study of the hydration of ions in aqueous electrolyte solutions is presented. Theoretical simulations of OH and OD stretching bands of isotopically diluted HDO molecules in a 0.44 m lithium formate solution have been performed. The positions of the atoms of the water molecules and the ions were taken from the trajectory file of a rigid-molecule room-temperature molecular dynamics simulation. V(r(OH)) potential energy functions were constructed as a sum of intra- and intermolecular energies and used in a variational calculation of the vibrational energy levels. Vibrational transition densities of states were calculated for HDO molecules in the first and second hydration shells of the ions. Infrared spectra of isotopically isolated HDO molecules in aqueous solutions of NaHCOO, LiClO4, NaClO4, Ca(ClO4)2, and Sr(ClO4)2 have been registered. The spectra were evaluated using an earlier developed double-difference method, where the number of ion-affected water molecules enters as a parameter in the analysis. In the present work, this number is obtained from the theoretical calculations, both for the Li+ and the HCOO- ion hydration. We find that OH/OD groups of water molecules in the second hydration shell of Li+, hydrogen-bonded to the first hydration shell, are affected by the ion. The earlier observed division of IR stretching frequencies for HDO molecules around cations into two distinct groups can now be explained by the presence or absence of such second-hydration-shell water molecules. For HDO molecules hydrogen-bonded to the HCOO- ions, the OH/OD frequency is lowered, compared to bulk water, for the OH/OD group involved in H-bonding to the ion, whereas the frequency is increased for the other OD/OH group, pointing away from the ion. The frequencies of HDO molecules surrounding the CH end of the formate ion are not influenced by the ion.