This paper contributes to the ongoing controversy over price and volatility spillovers across countries by providing new evidence with the futures data of the S&P 500 and Nikkei 225 index futures contracts from January 3, 1990 to April 16, 1996. Based on the two-stage symmetric and asymmetric GARCH models we document that both the U.S. and the Japanese daytime returns significantly influence the subsequent overnight returns of the other market. We find no signs of volatility spillovers between two international markets with the symmetric model. However, with the asymmetric models, we find that the magnitude of foreign negative shocks are different from the positive ones. The findings generally suggest that the two markets are more sensitive to the bad news originating in the other market. This nature of transmission between two markets would have important implications to the arbitragers who are trying to exploit the short-term dynamics of price and volatility movements across two security markets.