Rheological properties of amorphous hydrogenated styrene-butadiene copolymers (HSBC) were investigated. The structure corresponds to styrene-ethylene-1-butene terpolymers. Entanglement molecular weights (M-e) of 2380-3270 g/mol were obtained at 50 degrees C for HSBCs containing 49.5-68.9 wt % of styrene. These values were closer to polyethylene rather than polystyrene. The vertical shift factor, b(T), showed quite different temperature dependence from the classical expression of b(T) = rho T/rho(0)T(0), where rho and rho(0) are the densities at temperature T and a reference temperature T-0, respectively. This had also been observed in poly(ethylene-co-1-butene) and could be attributed to the temperature coefficient of unperturbed polymer chain dimension, kappa = d ln < R-2>(0)/dT, by using the packing model, The temperature dependence of b(T) indicated the temperature dependence of M-e for HSBCs. The M-e at 140 degrees C were estimated as 3100-4200 g/mol for HSBCs containing 49.5-68.9 wt of styrene, which was about 30% higher than at 50 degrees C. Plateau moduli obeyed the following equation: G(N)(ep)(0)(1/3)/rho(ep) = Sigma q(j)G(N)(j)(0)(1/3)/rho(1), where q(j) is the volume fraction of comonomer j, and G(N)(ep)(0), G(N)(j)(0), is the plateau modulus and rho(ep), rho(j) is the density of the copolymer and homopolymerj, respectively. This relation could also be applied to poly(ethylene-co-1-butene). The dependence of plateau moduli on backbone chain length suggested that styrene comonomer incorporation into ethylene-based polymers increases the trans conformation, while alpha-olefin incorporation increases the gauche conformation.