We describe the nuclear relaxation of protons by paramagnetic centers in glassy solutions of polymers. Both the protons and the paramagnetic radicals are on the polymers? and the solvent is fully deuterated. Two cases have been analyzed, ti?at when the relaxing centers are randomly distributed, and that when each polymer has a single center grafted at one end. The analysis was made for dilute and semi-dilute solutions of polymers. Experiments performed on poly-2 vinyl pyridine (P2VP) and on polystyrene yield results in agreement with theory, both as regards the NMR and the polymer models. (C) 1997 American Institute of Physics.