The article is devoted to the comparative study of peculiarities of translation of author's neologisms recorded in fantasy novels by British writer J. K. Rowling. The research was carried out on the material of translations from English into Russian and French made by professional translators. The article deals with the problems of literary translation in the fantasy genre. Author's neologism is one of the most important means of creating the fairy-tale reality and atmosphere of magic in the novel. This is a means to nominate magical creatures, phenomena, spells. Their transfer into a foreign language represents a special difficulty for the translator. To solve the problem, it is necessary to develop a pragmatic aspect of literary translation, to study the choice of fantasy translation strategy. The proposed technique in comparative studies of peculiarities of translating author’s neologisms is based on the difference between the two strategies of foreignization and domestication. The translation strategies have both positive effects and critical aspects. The author gives examples illustrating the use of various techniques and strategies for translating neologisms in the fantasy novel from English into Russian and French. The issues of pragmatic adaptation and quality of literary translation are analyzed. They are associated with strategy choice and methods of transfer of author's neologisms by means of a foreign language, such as transcription, transliteration, calques, functional replacement, neologism’s adaptation, creation of a translator's own neologism. Conclusions are drawn about the use of non-identical ways of translating neologisms by different linguists, about their choice of different strategies for specific transformations revealing the game of author's imagination.