In the context of globalization, through a growing process of economic integration among countries and financial markets, the interdependency among major world financial markets is more than evident The paper covers the most recent period 2000-2006 using monthly data and investigates and examines the short and long-run relationships between major world financial markets with particular attention to the Greek stock exchange. The research methodology employed includes testing for stationarity, both with the Dickey-Fuller and the Phillips-Perron tests, the use of a VAR model for the implementation of the Granger Causality test, and Cointegration tests according to Johansen-Juselious. The results confirm the dominance of the USA financial market and the strong influence of DAX and FTSE on all other markets of the sample. The influence of Germany and the DJ index is especially noticeable on the Athens stock exchange. We conduct cointegration tests with variance decomposition and estimate the impulse response functions.