In this thesis the so called convergence hypothesis is investigated using methods proposed by Phillips and Sul (2007 and 2009). The neoclassical growth model, more precisely, the extended Solow Model is the starting point of the analysis. Theoretical work leads to a non linear factor model, describing the log real income with a common factor describing the common development of all countries in a panel and an idiosyncratic component, measuring the relative share of the common component. As the idiosyncratic factor cannot be estimated straightly, so called relative transition paths are used for a graphical and quantitative analysis. Phillips and Sull propose the log-t convergence test for measuring convergence in a panel of economies. The observed inhomogeneity in the panels is the incentive for the cluster analysis. With two different clustering algorithms, the panels are divided into several convergent clubs. The panels analysed are a World Panel, an Africa Panel, a Europe Panel and a selection of 20 high developed OECD countries.