This article investigates the international information transmission between the U.S. and Greek stock markets using daily data from the Athens Stock Exchange (ASE) and the S&P 500 Index returns. It employs a bivariate exponential GARCH-t (EGARCH-t) that allows for both mean and variance spillovers between the two markets. It also performs cointegration tests on the long-run relation between these two markets and explores the possible common volatility feature in the spirit of Engle and Kozicki (1993). The results show no spillovers between these two markets for the conditional mean and variance. Also, the cointegration test shows that these two markets are not driven by a common trend. It appears that the U.S. and Greek stock markets are not related to each other, either in the short-run or in the long-run.