Quasielastic Neutron Scattering is a useful technique for obtaining information about the self-diffusion of water molecules in heterogeneous systems. Quasielastic neutron spectra have been obtained for hydrated brine shrimp (Artemia) cysts (1.2 g water/g solid) and water-polyox (1.67 g/g and 4 g/g) and deuterium-polyox (4 g/g) gels as a function of momentum transfer, Q. A triple axis spectrometer at the Oak Ridge research reactor, HFIR, was used to measure linewidths in the range .33-.1 THz at Q-values ranging from .5 to 1.9 A. A jump-diffusion model was used to describe the translational motion of the water molecules in both the brine shrimp and the polyox systems. The fitting routine employs Marquardt's algorithm which minimizes chi-squared in parameter space and determines parameters such as the Lorentzian linewidth as a function of Q . Results for the brine shrimp indicate that translational as well as rotational motion contributes to the linewidth. The measured linewidth is .329 THz at Q=.5 A, which is about twice the linewidth for pure water at the same O-value. Data for the 2% ployox in DgO mixture shows a large Lorentzian component. The magnitude of this component introduces large errors in the measurement of the motion of the water molecules in the water-polyox gels, due to the subtraction method used to determine the water spectra.