A person who wants to conclude an employment contract for the position of a scientist with an educational organization must first enter into a competitive relationship with this organization. The article analyzes in detail the competitive procedure for filling positions by scientists of educational organizations in the Russian Federation. Despite the similarities with the competitive procedure for the replacement of posts by professors and teachers, the competitive procedure for the replacement of posts by scientists has a number of significant features that have not yet been adequately covered in the legal literature. In this regard, the author dwelled on the features of the competitive procedure for filling positions by scientists in educational organizations and analyzed the main stages of the emergence of competitive legal relations of this category of workers. The winner of the competition receives the right to conclude an employment contract with an educational organization in the prescribed manner.