Interactions of O and O-2 with the Pd(111) surface are studied using spin-density-functional theory with gradient corrections. The investigation of potential energy surface of O atom on Pd(111) shows the face centered cubic site adsorption to be the most favorable. The diffusion barrier to an adjacent hexagonal closed pack site is 0.56 eV. Several adsorption trajectories are calculated for O-2 on Pd(111). We find that the molecule dissociation is either direct but strongly activated or precursor mediated with considerably lower barrier. Three precursor states are found and identified according to geometry, energy, and vibrational frequency. Two precursor states are energetically degenerate with only slightly different geometries. Density difference analysis reveals that the electronic structure of both the molecule and the nearest Pd atoms is modified during the adsorption. However, according to density difference analysis the molecules in the precursor states are neutral and the interaction between O-2 and the substrate resembles the donation-backdonation scheme.