The adsorption of oxygen and hydrogen (deuterium) on small neutral palladium clusters was investigated in a cluster beam experiment. The beam passes through two low-pressure reaction cells, and the clusters, with and without adsorbed molecules, are detected using laser ionization and mass spectrometry. Both H(2) and O(2) adsorb efficiently on the palladium clusters with only moderate variations with cluster size in the investigated range, i.e. between 8 and 28 atoms. The co-adsorption of H(2) and O(2) results in the formation of H(2)O, detected as a decrease in the number of adsorbed oxygen atoms with an increasing number of collisions with H(2) molecules. A comparison is done with an earlier similar study of clusters of Pt. Furthermore a comparison is done with what is known for sticking and reactivity of surfaces.