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Teachers of the gifted students should not only make an enrichment and accel-eration program for them but also pay attention to the development of analytical, crit-ical and creative thinking skills. Despite great interest for this issue in the last years, the topic of analytical and creative thinking is poorly considered in the textbooks for the gifted. In this article some methods, materials and programs of analytical, critical and creative thinking skills development, which are used in the USA, are described. The author analyses and systematize the methods and also suggests some ways of their usage in the Russian educational system. Purpose: to analyze and systematize methods, materials and programs, that are used in the USA for teaching gifted children analytical, critical and creative thinking, for development of their capacities of problem-solving and decision-making. Methods and methodology of the research: analysis, comparison, principle of the historical and logical approaches unity. Results: positive results of employment of analytical, critical and creative thinking development methods were shown in the practical experience of teaching and educating gifted children in the USA educational system. Results employment field: the Russian Federation educational system: schools, special classes and courses for the gifted children