The diffusion of water and the cross relaxation between water and cellulose in a hydrated paper system were followed with the Goldman-Shen and the pulsed-field-gradient stimulated-echo NMR pulse sequences as a function of moisture content. The diffusion coefficient measured along the plane of the paper sheet is very sensitive to the moisture content; more water leads to faster diffusion. The cross relaxation rate is independent of moisture content but high enough to severely influence the evaluation of the diffusion data. From the experiments, structural information about the porous network formed by cellulose microfibrils in the interior of the cellulose fibers is obtained.