Time-resolved small-angle neutron scattering (SANS) experiments were performed to study the later stage (i.e., the intermediate stage and the late stage) of spinodal decomposition (SD) of a critical mixture of perdeuterated polybutadiene (DPB) and protonated polyisoprene (HPI) with an LCST-type phase diagram and a critical temperature Tc = 36.1 °C. Time-sliced SANS intensity, S(q,t), is generally composed of the scattering due to growing domains, Id(q,t), and that due to the thermally induced local composition fluctuations inside the domain IT(q,t) where q and t are the scattering vector and time, respectively. S(q,t) as a function of q shows the “spatial crossover” such that at q much below and above a time-dependent wave-number, q,(t), it depends only on Id(q,t) and IT(q,t), respectively. The time evolution of the composition difference between the two coexisting domains, ΔΦ(t), was determined from IT(q,t), which was found to be consistent with the prediction of the scattering theory based upon the random-phase approximation. ΔΦ(t) was found to increase with t and reach a constant equilibrium value ΔΦe at t > tcr, where tcr is the crossover time from the intermediate to the late-stage SD. The crossover wavenumber, qs(t), also underwent a characteristic change at tcr.