Wide-angle X-ray data point to a three-phase structure in isotropic and drawn specimens of a homogeneous poly(ethylene-co-octene) (7.3 mol % 1-octene). In addition to the amorphous halo, the unoriented polymer exhibits Bragg reflections characteristic of the orthorhombic crystalline phase and an additional reflection that is assigned to the hexagonal mesophase. On stretching 800%, the degree of crystallinity increases from similar to 25% to similar to 50%, due mainly to the formation of smaller hexagonal crystallites, while the proportions of the orthorhombic and amorphous phases decline. Small-angle X-ray data reveal a distinct long period, pointing to the existence of lamellae that become oriented perpendicular to the draw direction. On releasing the specimen, there is a considerable permanent set (similar to 350% extension), and the crystallinity declines to similar to 30% as the hexagonal crystallites appear to revert to the amorphous structure. The results suggest that the hexagonal mesophase is formed by chain segments that have octene side chains, once these segments become oriented by deformation.