Sociolinguistic research on varieties of language and language variation, along with the necessity for meeting "equivalence" in terms of the appropriateness of the variety to the context have been well recognized in the formulation of a translation theory. However, the treatment of variation has always been restricted to dialect and has not encompassed the notion of diglossia. This paper stresses the need for research on the delineation of equivalence in diglossic languages, especially in literary translation where there is a continuous shift from one variety to another depending on the portrayal of characters and their interaction. Taking the classic definition of diglossia by Ferguson and the ensuing development of that definition, this paper raises some fundamental questions regarding the translation of language varieties in a diglossic situation, focusing on Arabic/English/Arabic translation. Examples are drawn from three main areas where there is a significant need: movies, literature, and liturgical literature. Major translation problems involved in the notion of appropriateness of the variety the situation are outlined, with suggestions offered for treating problems in the framework of a translation theory. Contains 27 references.) (SM)