The foreign subsidiaries of multinational enterprises are involved in two types of networks: an internal (corporate) network within the company including the headquarters and sister subsidiaries, and an external (inter-organizational) network of cooperating partners. Based on the concept of "dual embeddedness," this paper proposes a model explaining the role of internal and external relationships in developing innovation-related competitive advantages. A path analysis was conducted based on data from the Community Innovation Survey's 2010-2012 sample of enterprises - members of capital groups from 10 EU member states, mostly CEE (post-transition countries). The results show the positive influence of dual embeddedness on subsidiaries' innovation, leading to competitive advantages based on cost and on differentiation. A mediating role for external knowledge in the link of internal integration and competitive advantage is posited. External and internal relationships are not mutually exclusive; on the contrary, together they reinforce each other's impact on innovation performance. Internal integration plays a decisive role in building innovation-related competitive advantages based on cost, whereas external relationships have stronger influence on differentiation-based advantages. Therefore, the management of such firms should promote both types of relationships, considering their distinct roles in the process of building competitive advantages.