Molecular-beam techniques have been used to probe the sticking dynamics of molecular oxygen on Si(100) surfaces. The initial sticking probability S(O) is measured with Auger-electron spectroscopy as a function of surface temperature T(s) for various incident energies E(i). At E(i) = 0.09 eV, where the trapping-desorption process is dominant, S(O) decreases with increasing T(s). This fact indicates that sticking is predominantly a physisorption-mediated process. On the other hand, at E(i) = 0.9 eV, S(O) increases with increasing T(s). Since the direct inelastic-scattering process is dominant at this energy, this fact suggests that sticking occurs via direct access to molecular chemisorption which will successively go on to dissociative adsorption. Finally, we discuss a mechanism of sticking in terms of an electron transfer from Si to the incident O2.