The steady shear viscosities of two microphase-separated triblock copolymers, a polystyrene-block-polybutadiene-block-polystyrene copolymer (Kraton 1102) and a polystyrene-block-polyisoprene-block-polystyrene copolymer (Kraton 1107), were measured at various temperatures, using a cone-and-plate rheometer at low shear rates (ca. 0.01-10 s(-1)) and a capillary rheometer at high shear rates (ca. 5-5000 s(-1)). Tn order to investigate the effect of sample preparation on the viscosity, specimens of Kraton 1102 were prepared using two different methods : (a) solvent film casting and (b) compression moulding. Samples of Kraton 1107 were prepared only by compression moulding. In the present study we found that (a) for compression-moulded specimens the shear viscosities obtained using a cone-and-plate rheometer did not overlap those obtained using a capillary rheometer, while for solvent-cast specimens there was a reasonably good agreement between the two, and (b) the viscosities of solvent-cast specimens were much lower than those of compression-moulded specimens. This observation was explained with the aid of transmission electron micrographs, which were taken of ultrathin sections cut parallel and perpendicular to the direction of shear. We found from transmission electron micrographs that the application of steady shear flow affected greatly the morphology of Kraton 1102 having cylindrical microdomains of polystyrene phase, whereas it affected little the morphology of Kraton 1107 having spherical microdomains of polystyrene phase. Also measured were the complex shear viscosities of the two block copolymers at various temperatures. We have shown that neither time-temperature superposition nor the Cox-Merz rule is applicable to microphase-separated block copolymers.