The pulsed field gradient stimulated echo NMR technique is applied to the study of water diffusion in biological porous materials (a sheet of wood cellulose fibers and a packed bed of potato starch granules) consisting of randomly oriented domains with an anisotropic supermolecular organization. Expressions are presented for the probability distribution of apparent diffusion coefficients due to two- and three-dimensional powder distributions of domain orientations. The distributions are converted to echo attenuation curves with a method taking cross relaxation between the water and the solid matrix into account, Using a model in agreement with the structure and domain orientation known from other experimental techniques, it is found that the mean diffusion coefficient and degree of anisotropy (ratio between water diffusivity parallel and perpendicular to the structure director) at a level of hydration corresponding to approximately 90%, relative humidity are (1.68 +/- 0.03) x 10(-11) m(2)/s and 6.4 +/- 0.9 for cellulose and (7.8 +/- 0.1) x 10(-12) m(2)/s and 2.5 +/- 0.3 for starch, respectively. A systematic examination of different models for the diffusion coefficient distribution shows that the chosen models are not unique in describing the data. For the estimation of anisotropy, a physically correct model is required. The average diffusion coefficient can be determined with any reasonable model. not necessarily physically correct.