The relationships among structure and properties have been established in copolymers of ethylene and 1-octene, synthesized by a particular metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is, evidently, the comonomer content. However, the cooling treatment from the melt has been found to be also a very significant factor and, although its influence on the thermal properties is rather small, some structural parameters and the viscoelastic behavior are clearly dependent upon thermal history. These parameters include the degree of crystallinity, lattice constants, relaxation processes, stiffness, and microhardness of the samples. Regarding the viscoelastic behavior, the β relaxation is shifted to lower temperatures and its intensity is increased as 1-octene content raises. On the other hand, the α mechanism, associated with motions within the crystalline regions, is also moved to lower temperatures. Such a relaxation is only observed up to a certain 1-octene content in the copolymer.