The dissociative adsorption of oxygen on the (111) surfaces of platinum, palladium, and nickel has been investigated using nb initio local-spin-density calculations. For all three surfaces, adsorption is shown to be precursor-mediated and the structural, energetic, vibrational and electronic properties of the precursors are in very good agreement with the available experimental information. The investigation of the transition states shows that on Pt and Pd the barriers for dissociation are comparable to (or at sufficiently high coverage even higher than) the desorption barriers. In combination with large energies for atomic adsorption, this also leads to a high barrier for associative desorption-in agreement with observation. In contrast, the dissociation barrier For O-2 on Ni(111) is low and occurs already for a less stretched molecule. The trends in molecular and atomic adsorption and in the dissociation barriers are discussed in relation to the geometric and electronic properties of the substrate and to the sticking probabilities observed in molecular-beam experiments.