sigma-Bond metathesis reactions of water and methanol with palladium hydride and methyl complexes to yield hydrogen and methane, respectively, have been studied using ab-initio molecular orbital methods at the second-order Moller-Plesset (MP2) perturbation level. The calculations show that such reactions are feasible and that they can in some instances be competitive with an oxidative addition/reductive elimination sequence. A key factor is the presence of an additional lone pair not engaged in the initial bonding of the metal atom with the reacting water or alcohol. Another important controlling factor is the respective charges of the reacting entities. The importance of the choice and of the disposition of the ancillary ligands in the coordination sphere is emphasized.