By using quantum chemistry, the fundamental normal modes and the frequencies of ice Ih and room-temperature water clusters containing up to 15 water molecules are constructed. These normal modes are then used on the basis of assumed harmonic dynamics for analyzing the survival probability and energy decay of wave packets which reflect symmetric and asymmetric stretch excitations in single water molecules. Following symmetric stretch excitation, it is found that the wave packet survival probability and the OH stretch mode energy both decay on a sub-100-fs time scale in both phases. For asymmetric stretch excited states, the characteristic relaxation time is below 100 fs in ice Ih, but it is slower in liquid water. In both cases, it is found that the dynamics are truly many-body in character, since clusters of size similar to15 are required to converge the early time behavior of the OH mode relaxation processes. The results support the suggestion of Woutersen and Bakker (Nature 1999, 402, 507-509) that, in liquid water, intermolecular vibrational energy transfer occurs on a sub-100-fs time scale. The dynamics appear to be predominantly of harmonic character.