This paper investigates the asymmetric causal relationships between exchange rate and stock indices of Japan and Taiwan, respectively. M-TART is first found to be the most applicable model for adjustment to long-run equilibrium between the exchange rate and stock index for both countries. The evidence from our M-TART estimations supports the long-run equilibrium relationships between exchange rates and stock indices, but an asymmetric threshold cointegration relationship only exists in Taiwan, not in Japan. Further evidence from M-TECM Granger-Causality tests illustrates that no short-run causal relationship exists between the two financial assets. However, in the long-run, when the differences in the previous disequilibrium term are above their threshold value, a positive causal relationship running from stock index to exchange rate (by European quotation) in Japan supports the portfolio approach, whereas a positive causal relationship running exchange rate (by American quotation) to stock index in Taiwan argues for the traditional approach. Another interesting finding from our M-TECM estimations is that the speed of adjustment towards long-run equilibrium in relationship between stock indices and exchange rates is faster in the higher regime than in the lower regime for both countries' cases.