ENIdentifying gifted children and teenagers and their educational needs is one of the most relevant psychological and pedagogical problems, which is currently of great interest worldwide. Recognizing person's talents in education does not create added value by itself, the design of the educational process and the progress of the person's maturity related to diagnostics is much more valuable. The article analyzes how to educate gifted children, how different trends in the education of gifted children are developed, and what means are used to achieve affordable, high quality, modern education that meets the needs of a free civil society. The aim of the qualitative research was to reveal the views of Lithuanian and Ukrainian teachers about the peculiarities of the education of gifted students in gymnasiums. The data obtained during the research in identifying gifted students, the peculiarities of the education of these students and the effectiveness of educational tools revealed the educational difficulties faced by teachers and the opportunities for improving the education of gifted students in gymnasium. A qualitative study of teachers' views revealed that the identification of gifted students in the gymnasiums of both countries takes place when teachers pay attention to such student traits as creativity, critical thinking, etc.; teachers of both countries apply additional and individualized teaching methods when working with gifted students. The findings of the study revealed teachers' views about the effectiveness of educational methods of gifted students, the difficulties of educating gifted students, and provided practice-based suggestions for pedagogues who educate gifted students. Keywords: gifted education, gifted students, gymnasium, Lithuania, teachers, Ukraine. [From the publication]