Dynamical aspects of the dielectric response of supercritical water following an instantaneous charge jump on an initially neutral Lennard-Jones solute are investigated using molecular dynamics, The SPC model was used to describe solvent-solvent interactions, The simulation experiments were performed over the density interval spanning from 0.3 up to 1 g cm(-3) along the 645 K isotherm. Compared to room temperature results, the overall solvation process at high densities is an order of magnitude faster and becomes progressively slower as we move toward lower densities. In all cases, the nonequilibrium solvent responses present a bimodal behavior characterized by a fast inertial regime lasting a few femtoseconds followed by a much slower diffusional regime that dominates the long time behavior. This last portion of the response, which contributes to a small extent at high densities, accounts for the major contribution at lower densities, Predictions from linear response theory are quite accurate at high densities and become less adequate at lower densities, Instantaneous normal-mode analysis of the dynamics of the pure solvent and of the early stages of solvation are also performed; rotational modes provide the major contribution to the short time dynamics of the response at all densities.