Multivariate unobserved components (structural) time series models are fitted to annual post-war observations on real income per capita in countries in the Euro-zone. The aim is to establish stylized facts about convergence as it relates both to long-run and short-run movements. A new model, in which convergence components are combined with a common trend and similar cycles, is proposed. The convergence components are formulated as a second-order error correction mechanism; this ensures that the extracted components change smoothly, thereby enabling them to be separated from transitory cycles.