Sperm ultrastructure in the rare deep-sea cephalopod Vampyroteuthis infernalis is described, based on formalin-fixed material held in the Australian Museum (Sydney). The species is the sole member of the coleoidean order Vampyromorpha, which represents a level of organization intermediate between that of the Sepioidea-Teuthoidea and the Octopoda. Spermatozoa of Vampyroteuthis, the simplest observed in any cephalopod, exhibit the following features: (1) a spheroidal acrosome lacking any complex substructure; (2) a short (8.5 <latex>$\mu$</latex>m) fusiform nucleus with a deep (2.2-2.5 <latex>$\mu$</latex>m) basal invagination (containing an extensive plug of dense material); (3) two triplet centrioles arrange parallel to the sperm longitudinal axis; (4) a short (1 <latex>$\mu$</latex>m) midpiece composed of a triangular cluster of mitochondria surrounding the centrioles; and (5) a tail (length 130-135 <latex>$\mu$</latex>m) that is continuous with one of the centrioles (here considered as a 'distal' centriole). An annulus and membranous skirt are absent, though the coarse fibres do fuse into a ring at the tail-midpiece junction). These cells show some resemblance to sperm or spermatids of sepioids and teuthoids (spheroidal acrosome, short nucleus) but are also remarkably similar to midspermatids of Octopus (with the exception of the uncondensed nucleus in Octopus spermatids). Sperm morphology supports the current assignment of Vampyroteuthis to a separate coleoidean order - Vampyromorpha - and also suggests that a close link exists between the Vampyromorpha and Octopoda.