Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) has been used to study self-diffusion characteristics of water and oil in natural peanuts and in peanuts saturated with water. From the dependence on diffusion time of the echo decay due to diffusion, regions of completely restricted diffusion for the oil molecules were identified. The mean size and size distribution function of these regions were obtained. Combined analysis of diffusion data for peanuts with natural moisture content and for water saturated peanuts shows the cellular nature of these regions. The cell structure, consisting of a cell cavity surrounded by a double membrane was identified.