This paper emphasises that, for the less advanced European Union countries, FDI inflows are an important engine of convergence towards their more advanced counterparts. In general, CEECs and Cohesion countries hosting FDI tend to grow faster than those receiving few FDI. Not only the level but also the sectoral composition of FDI matters. Multinational corporations, by carrying out technically demanding production functions, have contributed to upgrade the production capacities of receiving CEECs and to increase the technological level of goods produced there. Competing on similar markets, but with higher wages and lower human capital endowments than CEECs, Portugal has lost its "comparative advantage" with the entry of CEECs as a possible destination of export-oriented FDI. This "diverting effect" explains a part of the disappointing performances of Portugal in terms of catching up. Thus, the relevant issue is no longer whether CEECs will follow an Irish or a Portuguese convergence scenario, but rather whether Portugal will converge or diverge towards CEECs.