This paper studies the relationship between the stock market and the exchange rate in several countries. The approach taken in the first part of this study is a linear VAR, to be compared in the following part to a MSVAR. The data is also analyzed by Granger causality tests in both contexts and a thorough description of the empirical results obtained is shown. The research uncovers a spread (but not constant over time) causality from the exchange rate and American stock market to the local markets of the different nations studied. The non-linear, time varying approach allows several considerations on the dynamics of the relationship. The markets analyzed are the Japanese, the British and the German (pre-Euro) market against the US Dollar and the US stock market. The frequency of the data used is daily.