Molecular dynamics computer simulations have been performed to analyze the dynamics of ionic solvation. Dilute solutions of Na+ and Cl- in methanol and in a nonassociated model polar solvent whose molecules have the same polarity as the methanol molecules, but that cannot establish hydrogen bonds between themselves, have been studied. An analysis of the solvent response to step changes of the electrical charge of the solute in the linear response approximation has been carried out by calculating the autocorrelation functions of the fluctuations of the electric potential at the position of the ion. It is proven that most of the relaxation occurs in a short time period, especially in the nonhydrogen bonded system. The long-time regime of the solvent response is considerably diminished in the nonassociated liquid. In order to investigate the role of the rotational motions of solvent molecules on the relaxation processes, the angular velocity correlation functions have also been evaluated.