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 H2 or CH4. The reaction of H2 on defect sites occurs at low temperature (ca. 25 degrees C) on two types of Al atoms of low coordination numbers, AlIII or AlIV, to give AlIV-H and AlV-H, respectively. The amount of defects as titrated by H2 at 25 and 150 degrees C is 0.043 and 0.069 site/nm2, respectively, in comparison with 4 OH/nm2). In contrast, CH4 reacts selectively at 100-150 degrees C on the most reactive AlIII sites to form the corresponding AlIV-CH3 (0.030 site/nm2). The difference of reactivity of H2 and CH4 is fully consistent with calculations (reaction and activation energy, DeltaE and DeltaE++).