A combined use of DFT periodic calculations and spectroscopic studies (IR and solid-state NMR) shows that a gamma-alumina treated at 500 degrees C under high vacuum contains surface defects, which are very reactive toward H-2 or CH4. The reaction of H-2 on defect sites occurs at low temperature (ca. 25 degrees C) on two types of Al atoms of low coordination numbers, Al-III or Al-IV, to give Al-IV-H and Al-V-H, respectively. The amount of defects as titrated by H-2 at 25 and 150 degrees C is 0.043 and 0.069 site/nm(2), respectively, in comparison with 4 OH/nm(2)). In contrast, CH4 reacts selectively at 100-150 degrees C on the most reactive Al-III sites to form the corresponding Al-IV-CH3 (0.030 site/nm(2)). The difference of reactivity of H-2 and CH4 is fully consistent with calculations (reaction and activitation energy, Delta E and Delta E-double dagger).