The dynamics of hyaluronate-based hydrogels has been investigated by quasielastic neutron scattering (QENS). Hyaluronate (HYA) has been compared, in the same conditions of temperature and polymer concentration, to a chemically modified form, HYADD, in which the backbone has been grafted with a hexadecyl (C-16) side-chain with a degree of substitution of about 2% (mol/mol). This modification increases the hydrophobicity of the polysaccharide and leads to a stable gel already at polymer concentration of 0.3% (w/v), yielding a viscosupplementation with less quantity of polysaccharide. The time-scale covered by our measurements probes both water and segmental biopolymer motions. In both systems, the local dynamics of the network in the ps time-scale is mostly due to local reorientational motions of side groups. Such motions are not significantly affected by the small amount of aliphatic chains forming the hydrophobic junctions in HYADD. The diffusivity of water in both HYA and HYADD coincides with that of pure water within the experimental uncertainty. This result confirms previous ones on the dynamics of water in HYA solutions and it is of relevance for biomedical applications of hyaluronate-based systems because it affects the diffusive processes of metabolites and their interaction with tissues.