Power spectra for the tsunamis of 13 October 1963, 20 October 1963, and 28 March 1964, as recorded at several stations in the Hawaiian Islands and at Midway, were obtained by digital methods. It was found that a given tsunami produced spectra at nearby stations which were somewhat similar for low frequencies (i.e., out to 1.6 c/ks), but that even this similarity disappeared between spectra from stations as far apart as Hilo and Honolulu (210 miles). Likewise, a given station gives its spectral imprint to tsunamis incident upon it, but only qualitative similarities are found. The time changes in spectra of a tsunami at a given station do not support any simple picture of a local response function. The energy decay curves show the arrival of reflected energy from (sometimes) identifiable sources. The time changes in the mean frequency of incident energy are not immediately explainable.