Styrene-b-ethylene-co-butylene-b-styrene triblock copolymers with variable styrene and ethyl branch contents have been prepared by hydrogenation of the butadiene block in the precursor poly(styrene-b-butadiene-b-styrene)s. Their thermal and mechanical properties and their viscoelastic behaviour have been determined in order to establish the influence of the structural parameters. Thermal transitions measured by differential scanning calorimetry and dynamic mechanical analysis show, for the first time, the peculiar characteristics of these copolymers, which present two relaxations, alpha and beta, corresponding to the grass transition of polystyrene and the relaxation of the elastomeric block, respectively. The nature of the beta-relaxation depends on the crystallinity of the system. Below 50% butylene content, it can be related with that found in polyethylene copolymers due to segmental motions in the interfacial regions. Above 50% butylene, the crystallinity has practically disappeared and the -EB- block behaves as an amorphous ethylene-butylene copolymer, and the beta-relaxation values can be assigned to the glass transition of this amorphous system. Both styrene and ethyl branch levels determine the ultimate properties. By increasing the styrene content, the modulus at low deformation and the tensile strength at break increase but the abrasion resistance and resilience decrease. The ethyl content does not affect either resilience or hardness, but the tensile properties decrease with increasing the branch level.