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Structure self-assembling in the spinodal decomposition (SD) of polymer blends in its late stage has been explored for a near-critical mixture of polybutadiene and polyisoprene by a time-resolved light scattering technique, with a particular emphasis on the time evolution of the interface structure. By analysis of a scaled structure factor F(x, t) ≡ I(q, t)qm(t)3 over wide ranges of a reduced scattering vector x ≡ q/qm(t) and time, it was found relevant to divide the late stage of SD into two stages, I and II. Here, I(q, t) denotes the scattered intensity as a function of the scattering vector q and time t. In the intermediate stage preceding the late one, F(x, t) became sharper with its peak at x = 1 increasing with t. However, as time elapsed, F(x, t) turned out to be universal for t, first in the range of x smaller than about 2 and then over the entire range of x accessible by the present experiment. The time interval in which the former occurred is defined as late stage I and the one in which the latter was realised is called late stage II. In late stage I, the average thickness of phase-phase interfaces decreases towards an equilibrium value and the time evolution of the interfacial area density Σ(t) does not scale with qm(t), i.e. the exponents γ and α in the power laws Σ(t) ~ t−γand qm(t) ~ t−α do not coincide (actually, α < γ). Late stage II corresponds to the process in which these exponents become equal and the interface thickness reaches equilibrium. Such conditions probably ensure the establishment of a complete dynamical scaling law in the SD process.