We present spectroscopic measurements of the full dielectric function of aqueous solutions of sodium chloride and lithium chloride at concentrations approaching their solubility limits at room temperature. We find that the dielectric properties of the two salts are rather different at THz frequencies. Whereas both the real and imaginary part of the permittivity of NaCl increases with concentration, we see that the imaginary part of the permittivity of LiCl (related to the absorption) decreases with increasing salt concentration. We relate these changes to the behavior of slow and fast Debye relaxation processes in the solutions.