Effects of adding a small amount of a block copolymer to polymer blends composed of the same constituent polymers as the block copolymer on the kinetics of early-to-late-stage spinodal decomposition (SD) were investigated by a time-resolved light scattering (LS) at three different temperatures in a deep quench condition. The early-stage SD for the blends with and without the block copolymer was well described by the linearized theory of SD over the small q range covered by the LS method. At each temperature, the coarsening process of the structure self-assembled via SD, as observed by the time changes of the peak scattering intensity I(m)(t) and the scattering vector q(m)(t), was slowed with increasing block copolymer content. For each blend the scaling postulate was found to be approximately valid; i.e., the time changes I(m) and q(m) at different temperatures fall onto respective master curves on the reduced plots: reduced intensity I(m) and reduced scattering vector Q(m) plotted against reduced time tau. However, the master curves on I(m)(tau) and Q(m)(tau) obtained for each blend depend on the amount of the block copolymer, thus showing a ''branch (or nonuniversality)'' on the reduced plot. The greater the amount of the block copolymer, the slower the coarsening of Q(m) and I(m) in the reduced time scale tau. The branching designated ''B-branching'' where B stands for block copolymer is due to a reduction of interfacial tension as a consequence of localization of the block copolymer at the interfaces during the ordering process.