Volumetric and microcalorimetric measurements of the adsorption of H-2, O2, CO, and CO2 on gamma-Al2O3 have been carried out. Amounts adsorbed at different temperatures in the range 195-673 K have been determined as a function of pressure and time. Heats of adsorption vs coverage have been measured at 315 K, and in some cases also at 263 K. Hydrogen and oxygen adsorbed weakly on gamma-alumina; an activated, somewhat stronger adsorption of these two adsorbates appeared at 300-400 K, and a highly activated oxygen reaction with the alumina surface began at around 573 K. Carbon monoxide adsorption was stronger than that of hydrogen or oxygen, and reached higher coverages. CO adsorption was mostly due to a weak surface carbonyl bond although formate species also appeared on the surface. Carbon dioxide adsorption on gamma-alumina produced three energetically different species which were identified with the help of infrared spectroscopy data as (1) very strongly held surface carbonate, (2) surface bicarbonate formed by reaction with, and whose number therefore depends on the number of, hydroxyl groups, and is slowly converted into carbonate, and (3) weakly adsorbed CO2. Adsorption calorimetry results give support to the conclusions obtained from the analysis of volumetric isotherms, showing that isotherms themselves can yield valuable information on several details of the adsorption process.