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Introduction. Nowadays, the development of national competitiveness depends on many factors, but the quality of human capital is first of all. One of priority tasks of education system in Russian Federation is search and support of gifted children and teenagers: creation of conditions for their productive education, full upbringing and optimum development of their abilities providing further maximum self-realisation of a person. Today, however, the implementation of these requirements is real only in megalopolises, large regional centers, but not in small cities, which have no sufficient resources and environment conditions, cultivating potential of every gifted child, especially in the case of art talent. The shortage of highly skilled teachers and cultural industry, weak involvement into cultural life (inability to attend concerts, theatrical performances, exhibitions, etc.), very limited access to participation in creative competitions, olympiads, competitions – all this negatively affects motivation engage in art activity and can lead to serious personal crises and waste of talent. The aim of the article was to reveal the content of models of work with musically gifted children, who have certain problems that block their creative development. Methodology and research methods. The research was based on personally-oriented and system-based approaches to education of gifted children. The authors considered the ideas of Russian and foreign researchers about the need for pedagogical support of gifted children, who have problems in general and cultural development. The methods of theoretical analysis of scientific and scientific-methodological resources, comparative analysis of the results of practical activity, ge-neralisation, oral and written survey and modeling were employed. Results and scientific novelty. The most common challenges of the development of gifted children, who live in towns, are revealed: lack of motivation for creativity and further development; a low level of general culture; tense atmosphere in family, which is expressed most often in the inattentive relation of parents to interests and abilities of a child. The specialists of Ural Musical College and children’s art schools of the city of Ekaterinburg and Sverdlovsk region developed and approved the models of social and pedagogical support of gifted children to eliminate the causes of their failures in education. According to the classification of problems in the development of gifted children, three types of personally-oriented models are offered: 1) motivation to creative activity, 2) cultural self-enrichment, 3) conditions for creative development of the child in family. The realisation of each model should be based on close cooperation of staff members of specialised centres (e.g. in musical college) for work with musically gifted children, teachers of children’s music schools, teachers of educational institutions of towns, children and their parents. The most effective activities, contributing to the solution of the formulated tasks of each model, are identified: concert-performing, cultural-educational and analytical (fixation and reflection of the results of creative development). Practical significance. The experimental testing of models proved the efficiency and possibility of complete and partial use of their components in Russian schools in order to manage the process of development of musically gifted pupils. © 2019 Russian State Vocational Pedagogical University. All Rights Reserved.