The article highlights the controversial issues of executive branch dualism in Ukraine and highlights the problems of the dualistic nature of the competence of civil-military administrations. It is noted that since the proclamation of Ukraine’s independence and up to now, political and legal discussions have been taking place around the problems of executive power organization. It is emphasized that the origins of the problem of executive dualism should be sought from the formation of the system of public authorities in Ukraine in the 90s of the twentieth century. During this period, there was a rather complicated political struggle and a search for the most optimal model of building a system of state authorities, which certainly affected the construction of the executive branch, and gave rise to a number of problems related to the dualism of power. The author emphasizes that the problems of dualism in the sphere of higher authorities have caused the same problems in the system of executive authorities and their relations with other types of public authorities, in particular, with local self-government bodies. The author analyzes and summarizes the problems in the field of relations between local public authorities (local executive authorities and local self-government bodies) and identifies the following: conceptual problems of delimitation of powers between certain executive authorities and local self-government bodies, legal problems of delimitation of powers between certain executive authorities and local self-government bodies; institutional problems. It is emphasized that dualism was also observed in the course of functioning of civil-military administrations, although in this case it was of a slightly different nature, which is due to the special legal status of the latter. The author identifies the peculiarities of such dualism. The author emphasizes the need to improve the legal framework for the functioning of civil-military administrations, to carry out institutional changes (search for a model, structure, etc.), to organize work, to apply new forms and methods of management, and to conduct further scientific research.