This paper examines the empirical relationship between five European stock market indices
and the US market in a smooth transition regression (STR) framework. Due to globalization
of economies the motivation is that the New York market has exerted substantial influence on
international markets in post-October 1987 period. The results show that the US market plays
indeed an important role and determines stock market asymmetric behaviour in Europe,
though non-linearity is not particularly strong.