Elastic and quasielastic neutron scattering experiments have been used to investigate the hydrogen bonding network dynamics of hydration water on hydrophilic and hydrophobic sites. To this end the evolution of hydration water dynamics of a prototypical hydrophobic amino acid with polar backbone, N-acetyl-leucine-methylamide (NALMA), and hydrophilic amino acid, N-acetyl-glycine-methylamide (NAGMA), has been investigated as a function of the molecular ratio water : peptide. The results suggest that the dynamical contribution of the intrinsic and low hydration molecules of water is characteristic of pure librational/rotational movement. The water molecule remains attached to the hydrophilic site with only the possibility of hindered rotations that eventually break the bond with the peptide and reform it immediately after. A gradual evolution from librational motions to hindered rotations is observed as a function of temperature. When the hydration increases, we observe (together with the hindered rotations of hydrogen bonds) a slow diffusion of water molecules on the surface of the peptides.