The single-particle relaxation dynamics of hydrogen atoms in different oxomolybdate Keplerate-type nanocages characterized by a (metal)30 icosahedron and a size of ≈2.5 nm were studied using incoherent quasielastic neutron scattering. Measurements were performed on a compound with a {Mo72Cr30} nanocage containing internal acetate ligands and a sodium cation coordinated to 12 water molecules. Because of the presence of the methyl groups of the acetate ligands, the related cavity is mostly hydrophobic and represents an interesting model system for investigating the properties of water molecules under confined conditions in contact with hydrophobic surfaces. The single-particle dynamics of both the methyl groups and the water molecules inside the cavity were studied and characterized to be thermally activated processes. The volume explored by the hydrogen atoms during their motions was also determined. Elastic scan measurements of the {Mo72Cr30} cage, in comparison with the {Mo72V30} cage, which has the same skeletal structure as {Mo72Cr30} but a hydrophilic interior, have allowed an investigation into the vibrational dynamics of the cages themselves and the determination of the effect of the cage polarity.