Amplified fragment length polymorphism (AFLP) markers were used to investigate the relationships among Polystachya accessions from a group of closely related pantropical tetraploids. Before starting with the fingerprinting analyses, the polyploid accessions were first included in a phylogenetic analysis using low-copy nuclear DNA data to establish their relationships, which confirmed that they belonged to a species group of closely related allotetraploids. Neo- and Palaeotropical polyploid accessions formed two hybrid clades with apparently independent origins. Sampling for the AFLP analyses included single accessions from much of the range of the genus and populations from Costa Rica (CR) and Sri Lanka (SL) to compare population structure and genetic diversity in these two areas in more detail. A splits graph of the complete AFLP data showed three major clusters corresponding to three sources of population sampling (P. concreta, SL; P. foliosa, CR; P. masayensis, CR), with individual accessions from Africa and Indian Ocean islands showing a closer relationship to P. concreta from SL than to the two CR species. Individual accessions from the Neotropics occurred in more isolated positions in the splits network, with little resolution. Some P. foliosa accessions clustered with P. masayensis, suggesting some hybridization between the two species, and this was confirmed by Bayesian structure analysis. However, the splits network, structure and analyses of molecular variance indicated a generally high level of genetic divergence between the two CR species, despite their recent hybrid origin, occurrence in largely the same localities and occasional hybridization. Polystachya foliosa from CR had a higher degree of population-level genetic structure (ΦST = 0.291) than P. masayensis from CR (ΦST = 0.161) and P. concreta from SL (ΦST = 0.138), possibly because of its occurrence within a larger and more environmentally diverse continuous range than the other two species. Genetic divergence between Neo- and Palaeotropical members of the pantropical tetraploid group of Polystachya and the nonmonophyly of P. concreta suggested that P. concreta s.l. should be split and the use of this epithet should be confined to the Neotropics (the type is from Martinique). Other names should be used in Africa and the Asian tropics. © 2011 The Linnean Society of London, Botanical Journal of the Linnean Society, 2011, 165, 235–250.