Ultra-high molecular weight polyethylene (UHMWPE) was irradiated with accelerated electrons (1 MeV in air) using high dose rates (> 25 kGy/min) and thin specimens (thickness 1 mm). Parts of the specimens were remelted (200 degrees C for 10 min; 150 degrees C for 0, 2, 10, 30, 60 min). All specimens were stored in nitrogen in the dark at 5 degrees C. Supermolecular structure, extent of crosslinking, oxidative degradation, and macroradical content were studied by a number of methods (SAXS, WAXS, SEM, DSC, FTIR, ESR, TGA, solubility experiments, image analysis). The results obtained with irradiated samples were compared with those obtained with irradiated and remelted samples. It was confirmed that crosslinking predominates over chain scission at very high dose rates, even if the irradiation is performed in air. Discrepancies concerning supermolecular structure changes in UHMWPE after irradiation and thermal treatment, found in various studies in the literature, are discussed. A simple model, which describes and explains all supermolecular structure changes, is introduced. An effective way of eliminating residual macroradicals in UHMWPE is proposed.