A molecular theory of frequency and wave-vector-dependent dynamic response functions of electrolyte solutions is presented. The theory is based on linear response theory and a set of molecular hydrodynamic equations. The theory properly includes the static and dynamic interionic correlations through ionic structure factors and van Hove functions. Analytical expressions for frequency and wave-vector-dependent charge, ion moment, and ion current susceptibilities are derived and evaluated. It is found that the dynamic response at finite wave vectors can be very different from that at zero wave vector (or at long wavelength). An important application of the present theory is also discussed where we have studied the dynamics of ion atmosphere relaxation around a newly created solute charge.