This work expands the classical Nelson and Winter model of Schumpeterian competition by including two sectors and a North-South dynamics, with a view to analyzing how different institutions and technological regimes affect the processes of convergence and divergence in the international economy. The results suggest that convergence may emerge out of the efforts for imitation in the South when the technological regime is cumulative. But when the regime is science-based, imitation is not enough for a successful catching-up. In this case convergence requires the South to invest in innovation as well. The work also analyses the robustness of the model results using Montecarlo techniques.