The degree of silane grafting and cross-linking of several high-density polyethylenes (HDPE) was studied. The results are compared with those of a low-density polyethylene (LDPE) and a linear low-density polyethylene (LLDPE). Molecular characterization was done by gel permeation chromatography. The differences in grafting and cross-linking performance are correlated to the different structural parameters of the polymers such as molecular weight, molecular weight distribution, polydispersity index (PDI), and branching. The results show that molecular weight plays the main role in silane-grafting and cross-linking performance. For samples with approximately similar PDI, the grafting level increased with both increasing number average molecular weight and weight average molecular weight, whereas the gel content increased with increasing weight average molecular weight. However, a zigzag relation was observed for the variation of grafting and cross-linking performances with PDI. The presence of long-chain branching affects the size of molecules and reduces the grafting efficiency due to coil contraction and more intramolecular entanglements. The order of the degree of grafting for the different polyethylenes investigated was LLDPE > HDPE > LDPE, whereas the order for the gel content was LDPE > LLDPE > HDPE. The presence of unsaturated groups led to increase in the grafting level. However, there is no overall rule based on the density of polyethylene. Different grades of polyethylene show different behavior depending on the silane and peroxide concentration. (C) 2011 Wiley Periodicals, Inc. Adv Polym Techn 30: 286-300, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/adv.20224