It is well known that Australian languages make heavy use of nominal juxtaposition in a wide variety of functions, but there is little discussion in the theoretical literature of how such juxtapositions should be analysed. We discuss a range of data from Australian languages illustrating how multiple nominals share a single grammatical function within the clause. We argue that such constructions should be treated syntactically as set-valued grammatical functions in Lexical-Functional Grammar (LFG). Sets as values for functions are well-established in LFG and are used in the representation of adjuncts, and also in the representation of coordination. In many Australian languages, coordination is expressed asyndetically, that is, by nominal juxtaposition with no overt coordinator at all. We argue that the syntactic similarity of all juxtaposed constructions (ranging from coordination through a number of more appositional relations) motivates an analysis in which they are treated similarly in the syntax, but suitably distinguished in the semantics. We show how this can be achieved within LFG, providing a unified treatment of the syntax of juxtaposition in Australian languages and showing how the interface to the semantics can be quite straightforwardly defined in the modular LFG approach.