The transition from a less advanced economy to a convergent economy is a subject that intrigues economists and, which they are trying to find explanations. This interest becomes more apparent when some developing countries are making this transition while other countries cannot start the process. This paper will outline a definition of the convergence concept, before analyzing the literature of the emergence factors. Then, it describes the convergence models of some Asian latecomers countries to find the determinants that led them to reach this level of growth. Finally, it proposes an alternative model of catch-up for Senegal, taking into account the lessons from the emerging economies and the current Senegalese environment.