Abstract Each complete MV-algebra is naturally equipped with a structure of a frame. For this reason, we shall call such MV-algebras MV-frames and investigate some of their main frame properties. We completely characterize algebraic MV-frames as well as regular MV-frames. In addition, we consider nuclei on MV-frames in general and on MV-frames of ideals of Łukasiewicz rings in particular. Finally, we use the Chang–Mundici functor to explore the frame structures of complete unital lattice-ordered groups. 2010 Mathematics Subject Classification. 06D35, 06E15, 06D50