This paper describes an ISO project which aims at developing a standard for annotating spoken and multimodal dialogue with semantic information concerning the communicative functions of utterances, the kind of semantic content they address, and their relations with what was said and done earlier in the dialogue. The project, ISO 24617-2 "Semantic annotation framework, Part 2: Dialogue acts", is currently at DIS stage. The proposed annotation schema distinguishes 9 orthogonal dimensions, allowing each functional segment in dialogue to have a function in each of these dimensions, thus accounting for the multifunctionality that utterances in dialogue often have. A number of core communicative functions is defined in the form of ISO data categories, available at http://semantic-annotation.uvt.nl/dialogue-acts/iso-datcats.pdf; they are divided into "dimension-specific" functions, which can be used only in a particular dimension, such as Turn Accept in the Turn Management dimension, and "general-purpose" functions, which can be used in any dimension, such as Inform and Request. An XML-based annotation language, "DiAML" is defined, with an abstract syntax, a semantics, and a concrete syntax.