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Recent molecular phylogenetic analyses prompted recircumscription of Pandanales into five families—Cyclanthaceae, Pandanaceae, Stemonaceae, and Velloziaceae, plus the mycoheterotrophic Triuridaceae—that were not hitherto regarded as closely related and so have not previously been compared in detail. Some species exhibit anomalous floral features, including apparently secondary apocarpy, loss of trimery, and an imprecise boundary between inflorescence and flower. Most noteworthy are the female reproductive structures of Triuridaceae, especially the "inside-out" flowers of Lacandonia. A phylogenetic cladistic analysis using 39 morphological characters of 23 genera spanning all five families of Pandanales yielded three fairly well-resolved and moderately supported most-parsimonious trees. Velloziaceae were sister to all other Pandanales. Cyclanthaceae and Pandanaceae formed a sister pair that was sister to Stemonaceae plus Triuridaceae. Triuridaceae were embedded within a paraphyletic Stemonaceae. Pentastemona was sister to all other Stemonaceae plus Triuridaceae, supporting earlier suggestions that this highly divergent genus should be recognized as a separate family, Pentastemonaceae. Kupea was robustly placed as the basally-divergent node of Triuridaceae, upholding an earlier hypothesis that the biovulate condition in Kupea could represent the ancestral condition for Triuridaceae. Contrasting models are outlined for interpretation of the unusual apocarpous female floral units of Triuridaceae, either as (1) highly reduced partial inflorescences (pseudanthia), (2) inflorescence-like flowers derived by carpel multiplication (delayed determinacy) from an ancestor with a single free carpel (with flowers similar to those of Croomia, but unisexual), or (3) flowers derived from a tricarpellate syncarpous ancestor (with flowers similar to those of Pentastemona, but unisexual) by loss of carpel fusion and carpel multiplication. The formerly unsuspected close relationship between Stemonaceae and Triuridaceae supports the second model. The indistinct inflorescence—flower boundary in Triuridaceae could be attributable to an overlap in genetic programs, resulting either from a partial loss of integrity in regulation of flower development or from extreme axial condensation associated with the mycoheterotrophic habit.