The physics of gas hydrates are rich in interesting phenomena such as anomalies for thermal conductivity, self-preservation effects for decomposition, and others. Some of these phenomena are presumably attributed to the resonance interaction of the rattling motions of guest molecules or atoms with the lattice modes. This can be expected to induce some specific features in the low-frequency (THz) vibrational response. Here we present results for low-frequency Raman scattering in a Xe hydrate, supported by numerical calculations of vibrational density of states. A number of narrow lines, located in the range from 18 to 90 cm(-1), were found in the Raman spectrum. Numerical calculations confirm that these lines correspond to resonance modes of the Xe hydrate. Also, low-frequency Raman scattering was studied during gas hydrate decomposition, and two scenarios were observed. The first one is the direct decomposition of the Xe hydrate to water and gas. The second one is the hydrate decomposition to ice and gas with subsequent melting of ice. In the latter case, a transient low-frequency Raman band is observed, which is associated with low-frequency bands (e.g., boson peak) of disordered solids.