We have performed a series of molecular dynamics simulations of water containing either a methanol or an acetonitrile molecule to investigate the pressure dependence of various dynamical properties of these hydrogen bonding solutes in aqueous medium under ambient and supercooled conditions. It is found that the tracer diffusion and orientational relaxation of both the solutes in supercooled water and also the orientational relaxation of methanol in ambient water show anomalous behaviour with application of pressure. However, the extent of anomaly is quite different for the two solutes which is attributed to their varying hydrogen bond properties in aqueous medium. (C) 2003 Elsevier Science B.V. All rights reserved.