The viscoelastic relaxation of linear styrene-butadiene-styrene triblock copolymer (l-SBS) and star styrene-butadiene-styrene triblock copolymer (s-SBS) with four arms were investigated with differential scanning calorimetry and dynamic rheological measurements. Three characteristic viscoelastic responses of l-SBS and s-SBS in the plot of the loss tangent (tan delta) and temperature at different frequencies (omega's), which corresponded to the relaxation of the polybutadiene (PB) block (peak I), the glass transition of the polystyrene (PS) phase (peak II), and the mutual diffusion between the PB blocks and PS blocks (peak III), respectively, were observed in the experimental range. Although x was 0.1 rad/s, a noticeable peak III was gained for both l-SBS and s-SBS. The dynamic storage modulus (G') of l-SBS showed two distinct types of behavior, depending on the temperature. At temperature (T) < T(2) (where T(2) is the temperature corresponding to peak II), G' of l-SBS displayed a very weak x dependency. In contrast, at T > T(2), G' decayed much more rapidly. However, G' of s-SBS displayed a very weak x dependency at both T < T(2) and T > T(2). Only near T2 did s-SBS decay with x a little sharply. These indicated, in contrast to l-SBS, that s-SBS still exhibited more elasticity even at T > T(2) because of its crosslinking point between the PB blocks (the star structure). In the lower x range, l-SBS exhibited a stronger peak III than s-SBS despite the same styrene content for l-SBS and s-SBS. The high tan d value of peak III for l-SBS was considered to be related to the internal friction among the PB blocks or the whole l-SBS chain, not the PS blocks. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 120: 2962-2970, 2011