The pico- and nanosecond dynamics of the globular protein P-lactoglobulin were investigated by means of quasielastic neutron scattering. To discriminate the possibly different dynamical behaviors of internal and external protein residues, the spectra of properly H/D exchanged samples, both dry and hydrated with D2O, were measured. In dry samples, inner and outer protein regions are found to provide equal contributions to the quasielastic scattering intensities, over the whole explored temporal window. On the contrary, their dynamical behavior becomes differentiated in the hydrated samples. In particular, in the nanosecond time scale, internal residues appear to be characterized by a higher quasielastic scattering intensity than that of the external ones. A reversed behavior is instead observed in the picosecond time range, where the highest contribution arises from external amino acidic groups. These results provide new experimental evidence of a diversified dynamical behavior displayed by internal and external protein regions. In addition, they point out that hydration water affects the dynamics of the whole biomolecule, rather than that of the solvent-exposed regions only.