Naturalized immigrants to the United States and their descendants are sometimes referred to as hyphenated Americans, a term that dates to the end of the 19th century and that reflects an earlier tendency in American English to hyphenate such forms as Irish-American, German-American, and
Mexican-American both as nouns and as adjectives. Contemporary usage frowns on hyphenating these constructions, especially when used as nouns; thus, The new mayor is an Asian American; she is the first Asian-American (or Asian American) mayor in the citys history. In the case of Native American, neither the noun nor the adjective is usually hyphenated.
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The term hyphenated American has itself come under strong criticism as suggesting that those so designated are not as fully American as unhyphenated citizens, and you would do well to avoid this term except in historical contexts.