The relationships between structure and mechanical properties have been established in several copolymers of ethylene and 5,7-dimethylocta-1,6-diene synthesized by a metallocene catalyst. A dependence with composition and polymerization temperature has been found for different structural and mechanical parameters. The branches cannot be incorporated into the orthorhombic crystal lattice and, consequently, structural parameters such as crystallinity and crystal size are considerably affected as 5,7-dimethylocta-1,6-diene content increases in the copolymer. These structural changes influence significantly the rigidity of the copolymers and a decrease of this parameter, determined from either storage modulus or microhardness, with increasing 5,7-dimethylocta-1,6-diene molar fraction is found. The location of the different viscoelastic relaxations is also strongly dependent on composition.