Solid-state molecular chain diffusion in linear high-density polyethylene (HDPE) is established as the dominant mechanism for the crystalline C-13 longitudinal relaxation at 60 degrees C, confirming previous work of Schmidt-Rohr and Spiess. A progressive saturation NMR experiment was undertaken on several samples of HDPE, where different degrees of cross-linking were introduced by electron irradiation. A decrease in the rate of recovery of the,crystalline signal was observed with an increase in cross-link density, as measured by gel fraction. As irradiation forms cross-links on the fold surfaces of the lamellae, this behavior cannot be explained through a conventional dipolar spin-lattice mechanism or C-13 spin diffusion. Transport of magnetization via chain diffusion to the amorphous region, where it experiences an efficient relaxation process, is consistent with the relaxation data and the Overhauser enhancement. As the gel fraction increased from zero to 87%, the effective diffusion coefficients almost halved from the nonirradiated sample (0.033 nm(2).s(-1)) to 0.018 nm(2).s-1.