First H-1 NOESY NMR investigations on adsorbed molecules are presented. Experiments have been carried out on allyl alcohol adsorbed on NaX zeolite with a loading of approximately four molecules per supercage. By application of magic angle spinning (MAS) on the sealed samples, all five magnetically inequivalent protons could be resolved spectroscopically. H-1 MAS NMR spectra in the temperature range from 260 to 420 K are reported. Cross peak and diagonal peak intensities of 2D NOESY spectra at room temperature for different mixing times have been measured. Subsequently the matrix of cross relaxation rates has been obtained by a single least mean square deviation fit to all 2D peak intensities. Errors in the determination of cross relaxation rates are discussed. Selected cross relaxation rates could be interpreted by isotropic reorientation of the allyl group with a correlation time tau(c) = (6.1 +/- 0.4) x 10(-9) s at a temperature of 300 K.