In this article the author describes the application o f a number o f the principles in teaching a foreign language linguistically gifted school students in the modern system o f additional foreign-language education on the basis o f which spe- S cial programs o f teaching this category o f pupils are under construction. They promote the development o f the abilities to work independently in gifted school students, the activization of the productive abstract thinking and the highest intellectual processes in them, the development o f the research abilities, the formation of the basic skills together with the highest intellectual operations in pupils, the saturation of training material by the tasks o f an open type, the active use of various forms o f the presentation and introduction of the results o f work in practice. The author emphasizes that in teaching linguistically gifted school students the important role plays mutual trust, culture, cooperation, tolerance in the system o f additional foreign-language education. It is necessary to create such an atmosphere which would help to remove psychological barriers of the communication, to develop pupils' mental abilities, to create foreign-language communicative abilities.

Keywords: a foreign language, linguistic endowments, a linguistically gifted school student, additional foreign-language education, humanitarian culture, reflection, a dialogue o f cultures, intercultural thinking.