The deformation mechanism of polystyrene-bloch-poly(ethylene-alt-propylene) diblock copolymer having soft, spherical microdomains composed of poly(ethylene-alt-propylene) block chains in a hard matrix composed of polystyrene block chains under large oscillatory shear deformation with a strain amplitude of 0.41 at an angular frequency of 0.0944 rad s(-1) was investigated by the synchrotron radiation dynamic small-angle X-ray scattering (SR-DSAXS) method at temperatures of 95 and 158 degreesC. The 2D SAXS pattern was detected with an imaging plate (IP) simultaneously with stress measurement on specimens with the purpose to elucidate a relationship between macroscopic properties of the system as revealed by rheological measurements and response of its mesoscopic structure to the applied deformation as revealed by SAXS measurements. The SAXS result indicated that the spheres are packed in a body-centered-cubic (bcc) lattice with a paracrystal distortion. The local strain amplitude actually imposed on the spherical microdomains (gamma (shere)) and that on the {110} lattice spacing (gamma (lattice)) were measured as a function of strain phase, strain cycle N at the two temperatures. Both gamma (sphere) and gamma (lattice) at each temperature decay with N, in parallel to the stress decay with N. The decays of gamma (sphere) and gamma (sphere) nith N at 158 degreesC are larger than those at 95 degreesC. At a given temperature the decay of gamma (lattice) is larger than that of gamma (sphere) The Lissajous pattern of shear stress versus shear strain obtained in the first cycle showed almost a linear stress response to the strain. However, the nonlinearity develops and increases with N, and this nonlinearity is larger at 158 degreesC than at 95 degreesC. The shear deformation under this experimental condition did not induce a strong preferential lattice orientation: The lattice orientation remain essentially unaltered with N.