Dielectric relaxation of aqueous solutions of micelles, proteins, and many complex systems shows an anomalous dispersion at frequencies intermediate between those corresponding to the rotational motion of bulk water and that of the organized assembly or macromolecule. The precise origin of this anomalous dispersion is not well-understood. In this work we employ large scale atomistic molecular dynamics simulations to investigate the dielectric relaxation (DR) of water molecules in an aqueous micellar solution of cesium pentadecafluorooctanoate. The simulations clearly show the presence of a slow component in the moment-moment time correlation function [Phi(M)(W)(t)] of water molecules, with a time constant of about 40 ps, in contrast to only 9 ps for bulk water. Interestingly, the orientational time correlation function [C-mu(t)] of individual water molecules at the surface exhibits a component with a time constant of about 19 ps. We show that these two time constants can be related by the well-known micro-macrorelations of statistical mechanics. In addition, the reorientation of surface water molecules exhibits a very slow component that decays with a time constant of about 500 ps. An analysis of hydrogen bond lifetime and of the rotational relaxation in the coordinate frame fixed on the micellar body seems to suggest that the 500 ps component owes its origin to the existence of an extended hydrogen bond network of water molecules at the surface. However, this ultraslow component is not found in the total moment-moment time correlation function of water molecules in the solution. The slow DR of hydration water is found to be well correlated with the slow solvation dynamics of cesium ions at the water-micelle interface. (C) 2004 American Institute of Physics.