The purpose of this thesis is to study the interactions among returns on the United States, Mainland China and Hong Kong stock markets, and examine the interactions of pre- and post-global financial crisis periods as whether the bankruptcy of Lehman Brothers on 15 September, 2008 will produce different impacts on three markets. This thesis is to take 3 stock indices, applying the time-series analysis techniques such as Unit root analysis, Granger causality test, Impulse response analysis and Forecast error variance decomposition. According to the empirical results: 1. The daily mean returns on three markets are negative before the bankruptcy of Lehman Brothers but Mainland China and Hong Kong make a positive daily mean returns after the bankruptcy of Lehman Brothers except the U.S.; 2. Granger causality test, the daily return on the U.S. stock market stills is the predictor to Mainland China and Hong Kong; 3. Impact response and Variance decomposition analysis, the shock to the U.S. has a larger impact to Mainland China compared with Hong Kong for Post-period relative to Pre-period. Mainland China and Hong Kong respond more to the shocks in the U.S. for Post-period relative to Pre-period. The daily returns on three stock markets are more interactive for Post-period relative to Pre-period.