In this paper, in order to clarify the stock return relations of Japanese investment styles and US investment styles after the Lehman bankruptcy, we investigate the dynamic return linkages of Japanese four kinds of stock indices and US three kinds of stock indices. Specifically, this study empirically inspects the dynamic effects of the Nikkei 225, Tokyo stock price index (TOPIX), and the Morgan Stanley Capital International (MSCI) Japanese value-and growth-style equity indices on the MSCI US value, growth, and standard equity indices. As analyzing methodology, we employ the threshold generalized autoregressive conditional heteroskedasticity (TGARCH) model, and as a result of our investigations, we obtain clear and consistent important findings as follows. (1) First, our examinations by the TGARCH model evidence that the Nikkei 225 and TOPIX have a stronger effect on the MSCI US standard stock index than on the MSCI US value-and growth-style indices. (2) Second, our explorations by the TGARCH model further reveal that the time-series evolution of the MSCI Japanese value-and growth-style indices also has a stronger effect on the MSCI US standard stock index than on the MSCI US value-and growth-style stock indices.