We measured the inelastic neutron scattering (INS) of a single crystal of KOD-doped D2O ice, and investigated the dispersion curves in a proton-ordered phase of ice Ih (ice XI) and ice Ih. The intensity maps of the INS show that ice XI and ice Ih have two phonon dispersion curves in 50-65 and 72-90 meV, which assigned to the librational vibrations of water molecules. The results indicate that the phonon dispersion curves caused by the collective motions of protons exist in ice, and that ice Ih has small domains with proton-ordered arrangements. (C) 2003 American Institute of Physics.