We investigate the time responses of liquids, which change from phonon-like oscillations to an exponential decay, by means of optical Kerr effect (OKE) spectroscopy. We find that the time when the exponential decay becomes dominant and its decay time are on the same order, meaning that the dynamics is non-Markovian for various liquids and temperatures. In addition, these times show a strong correlation with each other, suggesting that the fast response of low-frequency phonon modes plays an essential role for the slow dynamics of the relaxational mode. (C) 2002 Elsevier Science B.V. All rights reserved.