This paper examines the integration of stock markets in Germany, France, Netherlands, Ireland and UK over the January 1973- August 2008 period at the aggregate market and industry level considering the following industries: basic materials, consumer goods, industrials, consumer services, health care and financials. The analysis is practised by using correlation analysis, beta-convergence and sigma-convergence methods. beta- convergence serves to measure the speed of convergence and sigma-convergence serves to measure the degree of financial integration. We might expect priori that European stock markets have been more integrated during the process of monetary, economic and financial integration in Europe. We find evidence for an increasing degree of integration both at the aggregate level and also at the industry level, although some differences in the speed and degree of convergence exist among stock markets. To our surprise, there is a downward trend in convergence for certain industries in certain countries in 2000s; especially for those industries, which are more prone to regional shocks, such as health care, financials and consumer services. Moreover, the cross sectional dispersion in health care industry has not shown a regular descending trend. Additionally, EU wide factors can better explain the changes in returns than those of US.