We carried out dynamic mechanical measurements to investigate three different examples of block copolymers: styrene-isoprene diblock copolymers and styrene-butadiene-styrene and styrene-(styrene butadiene)-styrene triblock copolymers. Isochronal and isothermal measurements of the real and imaginary parts of the complex shear modulus were performed over wide ranges of temperature and frequency. The measurements showed the presence of an additional relaxation process appearing at temperatures higher than those of the glass relaxation of the polystyrene phase, which has been misinterpreted by some authors as an order-disorder transition. The frequency dependence revealed that this process was a relaxation process and did not belong to a first-order transition. Moreover, the influence of crosslinking via dicumylperoxide was measured, and we constructed complete master curves to confirm the presence of two relaxation processes. The high-temperature relaxation process was strongly suppressed by crosslinking. Therefore, it was possible to detect the glass relaxation process of the polystyrene phase in a precise manner. The results were compared with those of homopolymers.