This article deals with the problem of an author’s national identification if this author fits in two different literary traditions. West-Icelandic literature is a specific phenomenon that belongs to both Icelandic and American or Canadian literatures. The early Icelandic immigrants in North America (Stephan Stephansson, Gestur Pálsson, Torfhildur Þorsteinsdóttir, Jóhann Magnús Bjarnason) created the strong literary tradition in the native language, which was considered a part of the Icelandic writing culture. The descendants of the first generation of Icelandic immigrants (Páll Bjarnasson, Laura Gudman Salverson) wrote their books mostly in the English language but kept the connection to Icelandic poetry and prose and discussed actual Icelandic community problems. These authors generally had double self-identification as Icelanders and Americans. They did not lose their national identity in an alien cultural environment. The new stage of the development of West-Icelandic literature started when the young generation of Icelandic immigrants came to the USA and Canada in the second half of the 20th century. Kristjana Gunnars is one of the writers who was born in Iceland but in Canada started to write in English. Her first books, One-Eyed Moon Maps (1980) and Settlement Poems (1980, 1981), focused on problems of immigration and self-identification, but in the 1990s she left these themes and wrote primary novels and poetry not in touch with Icelandic topics. That was Gunnars’ way to the world literature. Nevertheless, she is identified by readers as an Icelandic author and classified by literary scholars as a Canadian-Icelandic writer because the works are considered a continuation of Icelandic rich lyrical and narrative tradition