As practice shows, the success of project implementation depends on the clear and integrated interaction between stakeholders, the project manager, and the movable context. Such an interaction exists on the level of mental spaces. If the mental spaces are congruent, in other words, all things are in the space of clear and univocal understanding of all aspects of the project, “are speaking the same language,” then project implementation is clear, exact, and in time. On practice, it is observed that full understanding is absent during project initialization and implementation and mental space cannot be congruent completely or is congruent partially. This situation exists during the implementation of the international projects, which involves working together with specialists from different countries. In this case, the project manager must organize interaction between different mental spaces. A research hypothesis consists of the assumption that the interaction between mental spaces of the movable context, stakeholders, and the project manager is carried out in a blended mental space. This space is temporary in relative to other mental spaces during the project life cycle; the project manager should manage this space through the usage of different skills. The research was carried out by scientific methods of theories of mental and blended spaces, and the theory of knowledge, i.e. theoretical and empirical research using project management approaches. The research’s results showed that organization of interaction in the blended mental space with using appropriate competencies of the project manager provides successful project implementation. The theoretical base of research is presented in the example of the implementation of one of the largest infrastructure projects in Ukraine: New Safe Confinement Construction.