Foreign firms may enhance a developing country's formation of know-how by exposing or directly transferring local entrepreneurs the productive ideas of developed countries. However, foreign firms may also reduce the domestic entrepreneurs' incentive to accumulate know-how by increasing their competition and reducing the returns to entrepreneurial skills. It is shown that if externalities drive the formation of skills, after openness, initial conditions determine if a country converges to one of two steady states or to exhibit non'monotone dynamics. If instead, the costs and benefits of skill formation are fully internalized, openness gradually removes the pre-existing sector, generates a new sector of domestic firms, and the country catches up with developed countries. In both models, convergence requires the destruction of pre-existent firms. The implications for empirical work are also discussed.