The article deals with the modern approaches of national and foreign researchers to the identification of important generic competences in the preparation of Doctor of Philosophy degree students. In modern society, the role of science is constantly growing. Science becomes a peculiar identifier of the society development, a guarantor of its sustainable progress, and a driving force of rapid changes in all spheres of human activity. Due to science, the world is changing rapidly, and with it, the demands to the specialists are also altering. The problem of determining important competences that employees need to master has become one of the most urgent not only for educators, but also for employers, businessmen, and politicians. It is well known that the competences that are part of the generic competences are interconnected, over time they may lose their significance or, on the contrary, become more relevant. The rapid development of modern society requires the identification of new important knowledge, skills and abilities necessary for a highly qualified specialist, and the constant analysis of the structure of generic competences, including the one in the context of their significance and relevance. The problem of identification and development of important competences that future PhD students need to master during their studies in an educational and scientific program is one of the most urgent not only for educators, but also for society as a whole. The development of transversal competences gives the future scientist universality and opens up opportunities for the implementation of their projects both in the academic and non-academic spheres, and enables complete realization in public, political, economic and personal life. The analysis of modern scientific literature proved that the issue of training doctors of philosophy in the context of developing the structure of the generic competences, has been given considerable attention in the modern scientific space by national and foreign scientists. The scientific results under the review, regarding the central vector of our research, convinced us of the presence of different approaches to the determination of the studied competences. Scientists have presented clusters of such competences that differ in number and structure. It has been established that when determining the relevant competences in the context of the preparation of candidates for the degree of Doctor of Philosophy, researchers do not always use the names of competences for skills outlined in the List of general competences, based on the results of the Tuning project, which is recommended for use in the development of educational programs. As a result of it, there is a need for clarification of the semantic meaning of definitions and constructs chosen by scientists to outline the most significant competences in the training of students of the third educational and scientific level. Summarizing the presented approaches of scientists, we note that researchers most often emphasize the need to develop independence, the capacity to generate new ideas, skills in the use of information and communication technologies, the ability to communicate both orally and in writing in the native language, initiativity, the ability to work autonomously, and professional mobility. It has been found out that the competences which draw the attention of modern researchers as the most important ones are not in a state of contradiction with each other and do not exclude each other, but they can be considered as complementing each other, or even depending on each other. For example, academic mobility cannot be considered separately from the availability of knowledge and understanding of the subject area, understanding of the profession, the ability to apply knowledge in practical situations, skills in using information and communication technologies, the ability to conduct research at an appropriate level, the ability to be adapted and act properly in a new situation, the ability to work in an international context, etc.