For the purposes of this article, the authors define "multilingualism" as a state of general communicative proficiency in more than two languages; that is, a person is multilingual when he or she can fulfill his or her communicative goals in at least three languages. Bilingualism and trilingualism are thus seen as specific subtypes of a superordinate concept of multilingualism and not vice versa. The term TLA (Third Language Acquisition) represents the prototypical concept of the acquisition or learning of any language after the second language,whether the L3, L4, or even L7, as there is not merely a quantitative difference between SLA and TLA, but also a qualitative one. This difference is so fundamental that it needs to be covered by a new and different theoretical framework, or a substantially extended SLA model. In this paper, the authors first review the fundamentals of multilingualism--the models which have been developed to explain and describe multiple language acquisition--and then provide a brief critical overview of the German language research to date in this area. At present, there are four main models, each of which emphasises a different perspective. Taken together, they offer a fairly precise picture of what is known about TLA to date. (Contains 2 figures and 7 notes.)