Despite the wide-ranging applications of binary Rh and Ir oxides, their stability and trends in Rh and Ir oxidation states are not fully understood. Using first-principles electronic structure calculations, we demonstrate that the origin of the categorical stability of Ir(4+) is the relativistic contraction of the 6s orbital and, consequently, an expansion of 5d orbitals. Relativistic effects significantly stabilize Ir(4+)-containing metallic rutile IrO(2) over a wide range of O chemical potentials, despite the choice that Ir has of forming semiconducting corundum Ir(2)O(3). In contrast, Rh is found to display a wider stability range for corundum Rh(2)O(3) with Rh(3+) and a greater propensity for multiple oxidation states.