Summary. Introduction. The possibility of realizing the intellectual potential and development of students with enhanced abilities is actually ensured by creating conditions aimed at preserving and maintaining their health. Methods. In order to scientifically substantiate the system of accompanying students with increased mental abilities under the influence of risk factors of the educational environment on the basis of a multidisciplinary lyceum for gifted adolescents, a one-stage study of risk factors for the organization and intensity of the educational process and daily routine of students in grades 9-11 was carried out. To substantiate the application of the biofeedback method in the medical support system, the students were taught the diaphragmatic breathing technique, the effectiveness of which was evaluated on the basis of a comparative analysis of the functional state of the central nervous and cardiovascular systems, the psycho-emotional status of students before and after two weeks of functional biofeedback training. Results. It is shown that the risk factors for the health of students with increased mental abilities were the irrational organization of educational activities, its high intensity, as well as the violation of such health-saving components of the daily routine as night sleep and walks. At the same time, the analysis showed that the training loads contributed to the development of mental performance, and at the same time, increased tension in the regulatory systems of the students' body, which determined the need to develop a system to support students in the educational process. It was found that the implementation of diaphragmatic breathing training contributed to a 1.3-fold decrease in the level of anxiety among students, an increase in the number of students with satisfactory biological adaptation, against the background of a decrease in the number of students with reduced mental performance. Conclusion. The results of the study made it possible to scientifically substantiate and develop a system of accompanying students with enhanced abilities in the educational process, the implementation of which involves screening the diagnosis of the psychophysiological state of students, the formation of students of the "risk group" and "health group", the organization of a complex of corrective and health-improving and health-saving measures for them, aimed at increasing compensatory capabilities and psychophysiological reserves, strengthening and maintaining the health of students in the learning process.