In this paper NMR relaxation time investigations of water protons (H-1) and deuterons (H-2) in aqueous poly(ethylene glycol) (PEG) solutions are presented for the water content range of 3-90 wt %. The number of bound water molecules per PEG repeat unit is estimated to be one from the water relaxation times by using a model of fast exchange of water molecules between a bound and an unbound water fraction. For water contents lower than one water molecule per PEG monomer, large restrictions in polymer mobility occur which also influence water NMR relaxation. For these low water contents, small ranges of oriented PEG chains are present in the solutions resulting in observable quadrupole splittings in the H-2 NMR spectra.