Research on individual multilingualism and third language acquisition has expanded greatly in recent years. A theoretical correlate of this is the recognition of the fact that humans are potentially multilingual by nature, that multilingualism is the default state of language competence, and that this in turn has implications for an adequate theory of language competence, use and acquisition. Traditional second language acquisition (SLA) research usually treats all non-first language learners as second language (L2) learners. The recent focus on third language (L3) acquisition means that one has begun taking the complexity of multilingual learners' language background into account. This gives raise to reflection about some of the currently used basic terminology in the field, in particular how the concepts first, second and third language are understood. These terms are used variably in the literature. One approach, the common practice of labelling a multilingual's languages along a linear chronological scale as L1, L2, L3, L4 etc., is shown here to be untenable, being based on an inadequate conception of multilingualism. A different and arguably more satisfactory approach is based on the conventional dichotomy of L1 (established during infancy) versus L2 (added after infancy) and relates the notion of L3 to the presence of a more complex language background. The limitation to a three-order hierarchy involving the distinction between the concepts of L1, L2 and L3 is discussed and adopted as a working hypothesis, awaiting further research on this issue. Finally, the problems with the expressions first, second and third language have become more apparent with the emergence of research on L3 acquisition. Maybe the time is ripe to work for a change of these established terms? As possible replacements, primary, secondary and tertiary language are put forward for discussion. The paper stresses the need for reconsideration and clarification of the concepts L1, L2 and L3 from the point of view of multilingual language users and learners.