The disappearance of small languages occurs through an obligatory phase of collective natural bilingualism (i.e., bilingualism resulting from language contacts) and ends with the transition of the language community to a more widespread and promising language. The disappearance of languages is the most large-scale manifestation and realization of the desire of the language system for monolingualism; with individual natural bilingualism, this desire manifests itself as linguistic attrition. Mathematical modeling of the phenomenon confirmed the hypothesis about the instability of natural bilingualism: both the individual one, and the collective natural bilingualism providing «double» communication, are at the same time a phase of transition to monolingualism. Language keepers are monolinguals, therefore the main condition for the preservation of an ethnic language is the existence of a monolingual repository (e.g., a country where the majority of the population has one mother tongue). At the same time, monolinguals can have as many foreign languages mastered in a logical way. Optimal for the preservation of any ethnic language (not just a small one) is the monolingualism of preschoolers (indigenous language) and the introduction of the second, third, etc. languages at the school age in a logical way. Keywords: disappearance of languages, collective natural bilingualism, artificial bilingualism, language attritions, non-linear dynamics, mathematical modeling, unstable state, monolingual repository.