This paper analyses the risk spillover effect between the US stock market and the remaining G7 stock markets by measuring the conditional Value-at-Risk (CoVaR) using time-varying copula models with Markov switching and data that covers more than 100 years. The main results suggest that the dependence structure varies with time and has distinct high and low dependence regimes. Our findings verify the existence of risk spillover between the US stock market and the remaining G7 stock markets. Furthermore, the results imply the following: 1) abnormal spikes of dynamic CoVaR were induced by well-known historical economic shocks; 2) The value of upside risk spillover is significantly larger than the downside risk spillover and 3) The magnitudes of risk spillover from the remaining G7 countries to the US are significantly larger than that from the US to these countries.