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Principles of phylogenetic analysis (cladistics) are introduced with an examination of relationships among extant genera of Gnetales. The Gnetales can be supported as a monophyletic group, with Gnetum and Welwitschia more closely related to each other than either is to Ephedra. Characters of the progymnosperm Archaeopteris and 19 extinct and extant seed plant taxa are then reviewed as a basis for a cladistic analysis of their interrelationships. The seed plant taxa included are: medullosans, cycads, Lyginopteris, Cordaixylon, Mesoxylon, Lebachia, extant conifers, Ginkgo, Callistophyton, peltasperms, glossopterids, Caytonia, corystosperms, Bennettitales, pentoxylon, Gnetum, Welwitschia, Ephedra, and angiosperms. Preliminary analyses of relationships within conifers, glossopterids, and Bennettitales are also presented. Results suggest that seed plants are a monophyletic group, and Lyginopteris is resolved …