We have investigated multiple losses and overtones of H vibrations at Ni(11
1) by using electron-energy-loss spectroscopy. We mapped the energies along
the <(<Gamma>)over bar>(M) over bar direction of the surface Brillouin zon
e, and found two branches outside the two-phonon continua. This gives direc
t evidence of the existence of two-phonon bound states. Applying a one-dime
nsional model of coupled anharmonic oscillators, we derive the anharmonicit
y and discuss the localized property of the bound states.