Effective cooperation between the European Union (EU) and North Atlantic Treaty Organization (NATO) is not only desirable, but rather mandatory in this interdependent and interlinked World. The contemporary multifaceted security threats and challenges have diminished the importance of the national borders and made the members of the institutions almost equally vulnerable. Due to the inherited similarities among organizations, the perception of burden sharing seems natural. However, the existing cooperation framework leaves a big room for improvement. The article explores the factors limiting effective cooperation between the organizations and the analysis is derived from studying individual states’ (dual and non-dual members) behavior in shaping institutions’ interaction. The paper analyzes the roles of the EU and NATO during the Libyan crisis in the neighborhood of Europe and their interaction in Afghanistan – beyond the Euro-Atlantic area. The findings of the analysis show that some of the non-dual members of the organization “hold institutions hostage” ; fragmented positions of the dual members impede the elaboration of a holistic EU policy on crisis management (CSDP) and eventually, hamper formation of a joint EU-NATO strategic vision. Furthermore, lack of division of labor on the ground leads to overlapping of functions to certain extent and cooperation among institutions is better on operational rather than on the strategic level.