Abstract: By choosing stock index as the object of study， including London FTSE 100 stock index， French CAC 40 stock index， German DAX 30 stock index and Standard & Poors 500 stock index， which could represent well European and American stock markets， this paper first divides the time interval into the pre-crisis period， the subprime crisis and the European debt crisis， and then uses the state-space model and quantile regression to examine empirically the linkage between stock markets in Europe and the United States in the context of financial crisis. The results show that there is a long-term equilibrium relationship between European and American stock markets， and in the pre-crisis period U.S. stock markets have a short-term price guide relationship to European stock markets， but European stock markets do not have a short-term price guide relationship to U.S. stock markets. During the subprime crisis， the factors at economic base and market infection levels jointly determine the short-term price-guiding relationship between U.S. stocks and European stocks. And during the European debt crisis， there are mutual Granger causality in the stock markets， and the linkage between European and American stock markets is significantly enhanced. As a whole， the movements of U.S. stocks have greater impacts on the movements of European stocks.

Key words: financial crisis, linkage effect of stock market, state-space model, quantile regression