We have investigated multiple losses and overtones of H vibrations at Ni͑111͒ by using electron-energy-loss spectroscopy. We mapped the energies along the ⌫ M direction of the surface Brillouin zone, and found two branches outside the two-phonon continua. This gives direct evidence of the existence of two-phonon bound states. Applying a one-dimensional model of coupled anharmonic oscillators, we derive the anharmonicity and discuss the localized property of the bound states.