The high frequency behavior of the dynamic structure factor, S(Q,omega), of liquid and supercritical neon is investigated by inelastic x-ray scattering at different temperatures and pressure. The spectral evolution is described in terms of a single-relaxation-time viscoelastic model. The occurrence of a positive dispersion in the sound velocity is clearly visible in both investigated thermodynamic phases. The anomalies in the dispersive behavior deeply reduce at the higher temperatures, probably, as a consequence of important changes in the first shell interactions. More generally, the atomic dynamics is dominated by a relaxation process whose time scale is in the range of fast microscopic degrees of freedom (approximate to 10(-13) s), and whose strength and typical time scale stay constant over all the explored liquid and supercritical regions. (C) 2001 American Institute of Physics.