Temperature-dependent gas phase ion trap experiments performed under multicollision conditions reveal a strongly size-dependent reactivity of Pd-x(+) (x = 2-7) in the reaction with molecular oxygen. Yet, a particular stability and resistance to further oxidation is generally observed for reaction products with two oxygen molecules, PdxO4+. Complementary first-principles density functional theory simulations elucidate the details of the size-dependent bonding of oxygen to the small palladium clusters and are able to assign the pronounced occurrence of PdxO4+ complexes to a dissociatively chemisorbed bridging oxygen atomic structure which impedes the chemisorption of further oxygen molecules. The molecular physisorption of additional O-2 is only observed at cryogenic temperatures. Additional experiments and simulations employing preoxidized clusters PdxO+ (x = 2-8) and PdxO2+ (x = 4-7) confirm the formation of the two different oxygen species.