This work deals with the swelling properties of polyethylene gels prepared from long precursor ethylene/ethylene methyl acrylate (EMA) and ethylene/ethylene vinyl acetate (EVA) copolymers by random crosslinking between the EVA and EMA monomers repeated along the ethylene chains. An n.m.r. approach is proposed to characterize the statistical structure of dry and swollen gels. A power law relationship observed between the n.m.r. parameter and the swelling ratio suggests that the swollen gels obey a packing condition. The mechanisms of swelling of active statistical segments are investigated : a progressive change of chain segment conformation is evidenced upon swelling. A single master curve characterizing variations of chain statistics with the concentration is obtained for gels prepared at various cross-link densities.