In this work, a study of the influence of molecular structure on the viscoelastic behavior of melts of commercial polyethylene (PE) copolymers, particularly in extensional flows, will be performed. To enable this study to be performed, a series of four very low-density polyethylenes (VLDPEs) (film and blow molding grades) with different parameters of molecular weight (M W ), molecular weight distribution (MWD), and degree of long-chain branching (LCB) will be used. Experiments in shear flow (steady state and oscillatory regime) are complemented with experiments in uniaxial extension (constant strain rate and stress relaxation after a step strain). It will be shown that a qualitative correlation exists between both types of experiments; the stress relaxation experiments being particularly sensitive to the different molecular features of the polymers. In addition, the failure behavior in extension was also investigated and the results indicate that, within experimental error, the Hencky strain to failure is sensitive to the type of molecular structure but the corresponding tensile stress is not. POLYM. ENG. SCI., 45:984 -997, 2005.