Proton spin relaxation above the glass transition temperature and differential scanning calorimetry (DSC) have been used to investigate dynamical aspects of aging by a time-dependent change of the chemical composition in cis-1,4-polybutadiene samples. The polymer chains in bulk polybutadiene were cross-linked by exposure to ionizing radiation. The transition of the1H-NMR (nuclear magnetic resonance) signal from a liquidlike spin system response to a solidlike one is caused by cross-linking and network formation. This effect depends on the radiation dose. The description of the relaxation data is based on a stochastic model of translational diffusion of structural defects between fluctuating and fixed junctions of polymer chains. The assigned composite stochastic process has non-Markovian character. It is shown that the radiation yields changes in the constrained detect diffusion processes modeling the chain dynamic. Correlation time and memory time for the local and coherent segmental motion strongly depend on radiation dose. Based on this stochastic model, an understanding of aging processes on the molecular level is possible.