The decline of many minority languages, and the associated shift towards majority languages, raises the question of whether there is a point of no return or a 'threshold' in the process. The aim of this paper is to discuss the relevance of this concept. A static and dynamic model of minority language use are developed; these models offer a systematic relationship between sociolinguistic variables that are often considered in isolation. The concept of threshold is shown to be a relevant one, but it must be seen as a function of many variables rather than some unidimensional value. Such thresholds can be defined as functions of language attitudes, percentage of minority language speakers, and expectations-based adjustment by speakers to the observed decline in the vitality of the minority language. These results can be used to suggest language policies for the protection and promotion of minority languages.