Background: Lack of agreement about criteria and terminology for children's language problems affects access to services as well as hindering research and practice. We report the second phase of a study using an online Delphi method to address these issues. In the first phase, we focused on criteria for language disorder. Here we consider terminology. Methods: The Delphi method is an iterative process in which an initial set of statements is rated by a panel of experts, who then have the opportunity to view anonymised ratings from other panel members. On this basis they can either revise their views or make a case for their position. The statements are then revised based on panel feedback, and again rated by and commented on by the panel. In this study, feedback from a second round was used to prepare a final set of statements in narrative form. The panel included 57 individuals representing a range of professions and nationalities. Results: We achieved at least 78% agreement for 19 of 21 statements within two rounds of ratings. These were collapsed into 12 statements for the final consensus reported here. The term "Language Disorder" is recommended to refer to a profile of difficulties that causes functional impairment in everyday life and is associated with poor prognosis. The term, "Developmental Language Disorder" (DLD) was endorsed for use when the language disorder was not associated with a known biomedical aetiology. It was also agreed that (a) presence of risk factors (neurobiological or environmental) does not preclude a diagnosis of DLD, (b) DLD can co-occur with other neurodevelopmental disorders (e.g. ADHD) and (c) DLD does not require a mismatch between verbal and nonverbal ability. Conclusions: This Delphi exercise highlights reasons for disagreements about terminology for language disorders and proposes standard definitions and nomenclature. [This paper was also written by members of the CATALISE-2 Consortium.]