Neutron inelastic scattering studies on aligned crystals of Na x CoO 2 ⋅yD 2 O have been carried out. Significant scattering has been observed for phonons originating from the vibrations of the short-range ordered D 2 O molecules. No firm evidence for the magnetic fluctuations has been found for the Na x CoO 2 ·yD 2 O, while the very weak intensity modulation observed in the scans along (1/2, 1/2, l) suggests the existence of the antiferromagnetic fluctuations in the non-deuterated parts of the sample, the volume fraction of which is estimated to be about 26 %. The present results indicate that magnetic fluctuations, especially ferromagnetic ones are rather weak, in the deuterated system, which is consistent with the results of the NMR Knight shift reported by the present authors' group. We discuss the short-range ordered state of D 2 O, too by analyzing the observed diffuse scattering.