The southern segregates of Veronica (Hebe, Parahebe, Chionohebe, Dementia, and Detzneria) form a monophyletic assemblage of c. 144 species found in New Guinea, Australia, New Zealand, Rapa, and South America. Most of the species occur in New Zealand, where Hebe is the largest genus and a characteristic member of many vegetation types. Cladistic analysis of the Hebe complex, based on 45 characters and 22 terminal taxa, indicates that: (1) Hebe is monophyletic if Hebe 'Paniculatae' is excluded and H. formosa is included; (2) Parahebe is paraphyletic; (3) Chionohebe is monophyletic, but is part of a larger clade which includes alpine Parahebe and possibly the monotypic Detzneria; (4) Hebe 'Paniculatae', Derwentia, and New Guinea Parahebe are monophyletic basal groups in the complex. According to this study, recognition of monophyletic genera would require six genera in the complex, supporting the recognition of Derwentia and separation of Hebe 'Paniculatae' from Hebe. Leonohebe Heads is considered polyphyletic and is not accepted; new combinations are provided for two species of Leonohebe with no name at species rank in Hebe. Competing biogeographic hypotheses have implied (1) a Gondwanan origin, or (2) migration from South-east Asia via New Guinea. An origin in Australasia from Asian ancestors best explains the topology of the basal parts of the cladogram, but at least seven dispersal events from New Zealand are postulated to explain the occurrence of species of Hebe in South America and Rapa and Parahebe, Hebe, and Chionohebe in Australia. An hypothesis which did not allow dispersal would require that nearly all the evolution in the complex occurred before the Tertiary, and hardly any since.