© 2019 Elsevier Ltd The theory of the multinational enterprise (MNE) suggests that the subsidiaries of MNEs possess firm-specific advantages (FSAs) that can overcome their liability of foreignness (LOF). It also suggests that subsidiaries can gradually decrease their LOF over time as they learn more about the host country environment and develop better connections to local business networks. Accordingly, subsidiaries should outperform local firms not only at point of entry but also (and increasingly so) in the long run as LOF decreases. This paper challenges this received wisdom by using case-study methodology to argue that LOF may not decrease over time and, meanwhile, the FSA gap between local firms and subsidiaries may narrow. We focus on two types of FSAs (asset and transaction ownership) and three sources of LOF (complexity, uncertainty, and discrimination) to develop a theoretical framework for analysing the dynamic relationships between LOF and FSAs and show how local firms can outperform foreign subsidiaries over time. We use the case of the Chinese management software industry to illustrate the framework. Our findings have important implications for MNEs competing abroad as well as helping to explain the emergence of strong competition from local firms.