The stability of the group 13 hydrides in the oxidation state fill of the metal is analyzed by ab initio MP2 calculations suggesting that In2H6 and Tl2H6 are thermodynamically unstable in both the gas phase and the solid state. These compounds are, however, kinetically stable in the gas phase, and molecular structures and vibrational frequencies are predicted. Relativistic effects are discussed for the molecular properties of various thallium hydrides.