The adsorption Of O-2 on alumina-supported (Co)MoS2 catalysts and the subsequent mild oxidation of the (CO)MoS2 by O-2 have been studied by extended X-ray absorption fine-structure (EXAFS) spectroscopy. By analyzing the difference between spectra before and after O-2 exposure, small changes in the structure could be determined, which were not resolved using standard methods. At 20 degreesC on MoS2/alumina and (CO)MoS2/alumina, O-2 is chemisorbed at the edge of the MoS2 particles at a Mo-O distance of 1.73(2) Angstrom. The O-2 chemisorption results at the Mo edge indicate that, despite the large fraction of Co at the surface of the MoS2 crystallite in (CO)MoS2/alumina, some of the Mo atoms are exposed to the reacting gases. At 100 degreesC, there is partial substitution of S by O atoms in the Mo coordination sphere. The resulting decrease in both the Mo-S and Mo-Mo coordination numbers indicates partial disruption of the MoS2 crystallites. At 20 degreesC, O-2 chemisorption on (Co)MoS2/alumina also leads to displacement of the terminal Co-S bond and the formation of one Co-O bond at a distance of about 2.01(5) Angstrom. The terminal Co-S bond distance is 2.26(2) Angstrom and is significantly longer than the four bridging Mo-S-Co bonds, which are 2.18(2) Angstrom. At 100 degreesC, the latter are unreactive to O-2, although the Co ion coordination increases to about six, i.e., four bridging Co-S and two terminal Co-O bonds. The Co chemisorption results suggest that the terminal Co-S is the reactive bond that has been displaced by the oxygen adsorbate.