In literary theory, the works of (ethnic) minority authors – and similarly, the works of authors dealing with minorities–are often referred to as “assimilation narrative.” This term tends to suggest that minority authors, who write in the language of their country, seek a place in society through assimilation. Assimilation, however, means melting up in the majority nation by adopting all the values, customs and way of life characteristic of the majority, and abandoning, leaving behind, giving up the original traditional values, ethics, lifestyle, religion etc. of the minority. Assimilation means disappearing without a trace, continuing life as a new person, with new values, language, a whole set of new cultural assets. In this paper an effort is made to show that this is in fact not what many of the ethnic minority writers look for, so the term assimilation narrative is in many, although certainly not all, the cases, erroneuosly applied. It is justified to make a distinction between assimilation and integration narratives, as the two are not the same. In the paper examples are provided from Hispanic-American literature (Mexican-American, Puerto Rican and Dominican), across a range of genres from prose through drama to poetry, and also, examples are discussed when the author does in fact seek assimilation, as well as stories in which neither assimilation, nor integration is successful.