This paper applies the Phillips and Sul (2007) method to test for convergence in stock returns to an extensive dataset including monthly stock price indices for five EU countries (Germany, France, the Netherlands, Ireland and the UK) as well as the US over the period 1973-2008. We carry out the analysis on both sectors and individual industries within sectors. As a first step, we use the Stock and Watson (1998) procedure to filter the data in order to extract the long-run component of the series; then, following Phillips and Sul (2007), we estimate the relative transition parameters. In the case of sectoral indices we find convergence in the middle of the sample period, followed by divergence, and detect four (two large and two small) clusters. The analysis at a disaggregate, industry level again points to convergence in the middle of the sample, and subsequent divergence, but a much larger number of clusters is now found. Splitting the cross-section into two subgroups including Euro area countries, the UK and the US respectively, provides evidence of a global convergence/divergence process not obviously influenced by EU policies.