The segmental dynamics of poly(ethylene glycol) (PEG) chains adsorbed on the clay platelets within nanocomposite PEG/Laponite hydrogels was investigated over the tens of microseconds time scale, using combined solution and solid-state NMR approaches. In a first step, the time evolution of the molecular mobility displayed by the PEG chains following the addition to a Laponite aqueous dispersion was monitored during the aggregation of the clay disks and the hydrogel formation, by means of H-1 solution-state NMR. Part of the PEG repeat units were found to get strongly constrained during the gelation process. Comparisons between this time evolution of the PEG local dynamics in the PEG/Laponite/water systems and the increase of the macroscopic storage shear modulus, mainly governed by the assembling of the Laponite disks, indicate that the slowing down of the segmental motions arises from adsorbed PEG repeat units or chain portions strongly constrained between aggregated clay layers. In a second step, after completion of the gelation process, the molecular motions of the adsorbed PEG chains were probed by H-1 solid-state NMR spectroscopy. H-1 double-quantum experiments indicate that the adsorbed PEG repeat units, though reported to be frozen over a few tens of nanoseconds, still display significant reorientational motions over the tens of microseconds time scale. Using a comparison with a model system of amorphized PEG chains, the characteristic frequency of these segmental motions was found to range between 78.0 kHz and 100.7 MHz at 300 K. Interestingly, at this temperature, the level of reorientational motions detected for these adsorbed PEG chain portions was found to be as restricted as the one of bulk amorphous PEG chains, cooled at a slightly lower temperature (about 290 K).