We discuss from the perspective of relaxation dynamics the feasibility of recording NMR spectra of 33S nuclei bound to cross‐link junctions in cross‐linked elastomers (i.e. vulcanized rubber). Assuming the quadrupolar relaxation mechanism due to fluctuating electric field gradients, the calculations of transverse and longitudinal 33S relaxation times encompassing a large range of correlation times, static magnetic fields, and quadrupolar coupling constants reveal that both relaxation processes will constitute significant bottlenecks in recording the 33S spectra of cross‐linked elastomers inherently endowed with a large distribution of motional modes. In the rubbery state, the observable 33S NMR signal will result from motionally averaged, central transition magnetization of the 33S nuclei in cross‐link junctions involved in large amplitude, high‐frequency motions.