The interaction of O-2 with small Pd particles (2-10 nm) supported on an alpha-Al2O3(0001) single crystal under both ultrahigh vacuum (UHV) and high-pressure conditions has been studied by temperature-programmed desorption (TPD), temperature-programmed low-energy ion scattering (TP-LEIS), and X-ray photoelectron spectroscopy (XPS). A low O-2 exposure (30 L) at 500 K leads to surface oxygen adatoms on the Pd nanoparticles, which desorb in TPD as O-2 in a peak at similar to 880 K. Surface O adatoms on the smallest Pd particles move to subsurface sites starting at 400 K, and they almost all move subsurface by similar to 750 K, desorbing mainly at considerably higher temperature. The dominant oxygen species above 700 K is subsurface, implying that it is more stable than oxygen adatoms on Pd. Exposures of the Pd nanoparticles to 25 Torr O-2 at 373473 K readily convert the Pd to a species whose Pd XPS peak shifts by the same amount as the binding energy difference between bulk Pd and bulk PdO. We attribute this to PdO nanoparticles ( or a thin film of PdO on or under the Pd for the larger particles). The decomposition of the PdO on these nanoparticles to Pd in an equilibrium O-2 pressure of 10(-7) Torr does not occur until similar to 750 K, or similar to 200 K higher than the equilibrium decomposition of bulk PdO. This is attributed to the higher energy of Pd nanoparticles compared to bulk Pd and, for the larger particles, to the adhesion energy of the PdO film to the Pd, both of which stabilize the PdO on these Pd nanoparticles relative to bulk PdO. This PdO-like film on the larger particles may be similar to the ordered oxide thin film previously reported to form on Pd(111) but may also reside at the alpha-Al2O3 interface and be partially stabilized by adhesion to this interface.