Convergence in gross domestic product series of five European countriesis empirically identified using multivariate time series models that arebased on unobserved components with dynamic converging properties.We define convergence in terms of a decrease in dispersion over timeand model this decrease via mechanisms that allow for gradualreductions in the ranks of covariance matrices associated with thedisturbance vectors driving the unobserved components of the model.The inclusion of such convergence mechanisms within the formulation ofunobserved components makes the identification of various types ofconvergence possible.The common converging component model isestimated for the per capita gross domestic product of five Europeancountries: Germany, France, Italy, Spain and the Netherlands. It is foundthat convergence features in trends and cycles are present and areassociated with some key events in the history of European integration.