The NMR spin-lattice relaxation rate, T(,1)('-1), of water is independent of the Larmor frequency, (omega)/2(pi), in the normal rf range. However, T(,1)('-1) of intracellular water in biological systems, which accounts for as much as 80% of the cell mass, is frequency-dependent. This indicates that the NMR properties of water in the cellular environment are influenced by long-correlation time processes due to the interaction of water with proteins and other macromolecular constituents of the cell. In this research, the relaxation rate T(,1)('-1) of water in the Artemia (brine shrimp) cyst is examined as a function of: (1) the proton NMR Larmor frequency for .01 (LESSTHEQ) (omega)/2(pi) (LESSTHEQ) 500 MHz, (2) different cyst hydration levels from 0.12 to 1.25 grams water/gram dry solid, (3) temperatures of 22C and 5C. The frequency-dependence of T(,1)('-1) is interpreted in terms of a two-phase exchange model. One water phase is similar to pure water and contributes a small constant relaxation rate. The second phase is water closely associated with the surfaces of large molecules and termed "hydration water". A polymer-dynamics relaxation mechanism, which treats fluctuations of long-chain molecules in aqueous solution, has been proposed by Rorschach and Hazlewood to explain the relaxation in this second water phase. In one limit, this mechanism predicts a frequency-dependent relaxation rate proportional to (omega)('- 1/2). This particular dependence has previously been observed in other NMR studies on biological systems and is also observed in this study for Artemia cysts between 10 and 500 MHz. At lower Larmor frequencies, below 1 MHz, the relaxation rates of water in brine shrimp cysts are influenced by additional relexation mechanisms; translational diffusion of hydration water is one possibility.