We have studied the molecular reorientation and self-diffusion of water molecules in aqueous solutions of xenon in the approximate temperature range from 273 to 333 K using D-2 and H-1 magnetic relaxation and spin-echo techniques. In addition, we report on Xe-131 relaxation rates in this temperature interval. These data, in conjunction with data obtained recently by us for the self-diffusion of xenon, are evaluated in terms of scaling laws which are known to account for the peculiar behavior of transport and relaxation coefficients of pure water in the supercooled regime. In pure water these anomalies are strong enough to suggest a thermodynamic singularity at T-S = 228 K. The results for D-2 relaxation suggest that xenon shifts this singularity toward higher temperatures. An extrapolation toward the composition of the Xe x 23H(2)O clathrate yields T-S congruent to 260 K. Essentially the same figure is obtained from Xe-131 relaxation, which reflects the local dynamics of water molecules near xenon and may therefore serve as a measure of T-S in clathrate-like domains. This shift of T-S by added xenon confirms expectations that nonpolar solutes stabilize just those structures of water which are responsible for the anomalies observed in the supercooled regime. In this sense, xenon is acting like a negative hydrostatic pressure. It is however difficult to rationalize the data by a universal exponent, as is required by true scaling law behavior. As a further new feature we report on a decoupling of rotational and translational motions of water near T-S, which becomes apparent by largely different values for T-S deduced from relaxation and self-diffusion data. While reorientational motions reflect the slowing down of molecular motions associated with the approach to T-S, diffusion remains comparatively fast at the same temperature. This decoupling shows a striking resemblance with similar processes observed for other liquids near glass transitions.