We report a density-functional study of some properties of the dissociative interaction of hydrogen and oxygen molecules on small palladium clusters (n = 5, 7, and 10). The calculated physisorption and chemisorption energies are compared with those of the infinite (111) palladium surface. First, adsorption of atomic hydrogen and oxygen is investigated on the Pd5, Pd7, and Pd10 clusters. Second, the interaction between H2 (O2) and the small Pd5 cluster is examined and compared to the process occurring on an infinite (111) surface. Finally, the simultaneous adsorption of two hydrogen (oxygen) atoms is analyzed in detail. As shown in a previous work, the binding energy of the first hydrogen (oxygen) atom does not depend significantly on the cluster size, and small two-layer clusters (n ≤ 10) can be used to determine with accuracy the interaction of atomic adsorbates with an infinite (111) palladium surface. In this study, we show that the dissociative chemisorption of H2 and more especially of O2 on a small palladium cluster may lead to erroneous binding energy: the cluster's size may prevent an accurate description of the adsorbate-adsorbate interaction as a function of their distance. It is demonstrated that a good choice of both the size and the shape of the cluster is preponderant for a good description of the dissociative adsorption of H2 and O2 on an infinite (111) surface.