We have investigated the microdomain structure and viscoelastic properties of polystyrene-block-poly(ethylene-co-(ethylene-propylene)-block-polystyrene copolymer (SEEPS-1)/paraffinic oil (Oil-1) blends. The SAXS results revealed that, with increasing oil content, the structures change from a lammelar microdomain for SEEPS-1/Oil-1 = 100/0 to a hexagonally packed cylindrical microdomain for SEEPS-1/Oil-1 = 75/25 blend, and furthermore change to a spherical microdomain packed in a cubic lattice for SEEPS-1/Oil-1 = 50/50 and 25/75 blends. SEEPS-1/Oil-1 = 100/0 and 75/25 blends held each same microdomain structure below 300 A degrees C. In contrast, SEEPS-1/Oil-1 = 50/50 and 25/75 blends, respectively, exhibited order-disorder transition temperature (T (ODT)) at 210-220 A degrees C and 150-160 A degrees C. Below T (ODT), the microdomain structures did not change. Corresponding to the SAXS observations, the viscoelastic responses showed that the dynamic storage modulus G', respectively, is proportional to omega(1/2), omega(1/4)similar to omega(1/3), and omega(0) at low frequencies for SEEPS-1/Oil-1 = 100/0, 75/25, and 50/50 and 25/75, indicating lamellar, cylindrical, and spherical microdomains The time-temperature superposition was applicable on the ordered state, and the activation energy obtained from the shift factors was roughly independent of blend composition (in other words, microdomain structure), suggesting that the viscoelastic responses are due to the presence of defects of long range order of microdomain structures.