Abstract: This paper examines the existence of long-run benefits of the international diversification in the equity markets of the US, Greece, UK. The study which spans 11 years uses monthly data based on closing values of the general indices of Dow & Jones Industrial Average, FT All Share and Athens General Index. The examined period is based on a transitive stage of adaptation in the European equity markets after the end of 1999. The objective of this study is to present and analyze the long-run relations before (1994-1999) and after the stage of advancement and the institutional changes (2000-2005). For the analysis, the method of Engle & Granger is basically used, while in the cases of marginal results, the Johansen approach seems to be essential.