Vibrational states of H adsorbed on Ni(111) have been investigated by means of electron energy loss spectroscopy (EELS). In addition to the symmetric (ν_s) and asymmetric (ν_as) fundamental modes, the corresponding overtone structures are clearly detected. The overtone of ν_as, the predominantly parallel-polarized mode, exhibits a doublet structure at 0.5 ML, which is interpreted to result from the delocalization of the excited vibrational states. On the other hand, at high coverage (1.0 ML), the repulsive interactions between the adsorbed hydrogen promote the localization of the vibrational states, and the vibrational excitations are found to be collective (adsorbate phonons). The phonon dispersions are measured along the Γ⁻M⁻ direction of the surface Brillouin zone, where we find the evidence of the two-phonon bound states. Applying a one-dimensional model of coupled anharmonic oscillators, we derive the anharmonicity and discuss the localized property of the vibrations.