The partial differential cross section for the scattering of thermal energy neutrons from liquids and solids contains information about the diffusive motion of the nuclei. This experimental method is known as quasielastic neutron scattering (QNS). We have used QNS to study the effect of macromolecules and supramolecular structures on the diffusive motion of water in four systems: pure water, agarose gels, poly(ethylene oxide) (polyox) solutions, and the cyst stage of the brine shrimp (Artemia salina). The QNS spectra were studied using 0.95THz neutrons for values of the momentum transfer in the range 0.7(ANGSTROM)('-1) to 1.9(ANGSTROM)('-1), and energy transfers in the range -0.2THz to 0.2THz. Agarose gels were studied using a gel of 20% agarose in water by weight, and 20% agarose in deuterium oxide. Polyox solutions were prepared consisting of 20% polyox in water and 18.5% polyox in deuterium oxide (equivalent to 20% polyox in water). Brine shrimp were studied at hydrations of 0.10, 0.31, 0.78, and 1.20 grams of water per gram of dry brine shrimp. We have interpreted our data using the simplest heterogeous model for water in complex systems, the "bound-free" model. Analysis of QNS line shapes permits separation of the contribution of the tightly bound protons in the agarose and polyox from protons in the water. This analysis has allowed us to estimate the number of grams of water bound per gram of dry solid (c). For agarose c = 0.64 (+OR-) 0.26. The agarose results are in good agreement with previous nuclear magnetic resonance (NMR) studies of the diffusion coefficient. For polyox c = 1.46 (+OR-) 0.64. For the two highest brine shrimp hydrations c = 0.11 (+OR-) 0.07, but c decreased as the hydration decreased for the two lowest hydrations. The latter result is consistent with the results obtained by other workers with NMR. The free component in all of these systems showed deviations from the behavior of pure water. These deviations were all toward more "solid-like" behavior.