Ab initio pseudopotential calculations of Cu/Al2O3 and Au/TiO2 interfaces have revealed strong effects of interface stoichiometry. About the Cu/Al2O3 system used for coatings and electronic devices, the interfacial bond of the O-terminated (O-rich) Cu/Al2O3(0001) interface is very strong with ionic and covalent Cu-O interactions, although that of the Al-ternlinated (stoichiometric) one is rather weak with electrostatic and Cu-Al hybridization interactions. About the Au/TiO2 system with unique catalytic activity, the adhesive energy between non-stoichiometric (Ti-rich or O-rich) TiO2 (110) surface and a Au layer is very large, and there occur substantial charge transfer and orbital hybridization, which should have close relations to the catalytic activity.