The comparative functional morphology of the flight apparatus, the male secondary copulatory apparatus and the female ovipositor of Odonata are described. The investigations lead to a reconstruction of the evolution of the different mechanisms and contribute to the phylogenetic systematics of Odonata. — 1 — Although the flight apparatus of the three main groups of Pterygota (Odonata, Ephemeroptera, Neoptera) show fundamentally different features, inspection of the functional morphology has revealed that the differences are not unbridgeable. This comparison established new homologies and resulted in the reconstruction of an ancient flight apparatus of Pterygota (“Ur-Flugapparat”). The extant types of flight apparatus of Odonata, Ephemeroptera and Neoptera — provided with highly autapomorphous characters — can be derived from the “Ur-Flugapparat” in three functionally different lines of evolution, which are mutually exclusive. It may be concluded that flight ability has evolved only once, supporting the hypothesis of a monophyletic origin of the Pterygota. Although the problem of phylogenetic relationships between the three subgroups of Pterygota remains unsolved, there are indications that Ephemeroptera and Odonata are sister groups. — 2 — In the “Ur-Flugapparat” the dorsolongitudinal muscles presumably were used to produce an arching of the tergum during the downstroke (“tergal arching mechanism of flight”). This ancient function of dorsolongitudinal muscles has been modified fundamentally in the Odonata. Abandoning the use of meso- and metathoracic dorsolongitudinals as power stroke-muscles, the unique indirect-direct flight machinery of Odonata was developed — powerful (but nearly independent) — in both flight segments. — 3 — The evolutionary developments of the flight apparatus within the Odonata have mainly concerned the mechanisms of wingstroke-plane alteration of the fore- and hindwings, leading to two different main types of fliers: “precision-manoeuvre fliers” (Zygoptera, Anisozygoptera) and “forward-thrust fliers” (Anisoptera). — 4 — Dragonflies use three non-homologous parts of the male secondary copulatory apparatus as a functional “penis”: the ligula (in Zygoptera), the hamuli posteriores (in Anisozygoptera) and the vesica spermalis (in Anisoptera). The zygopteroid mode of spermtransfer via the ligula is thought of as the primary mode. An attempt has been made to reconstruct a continuous transformation series between this type and the different types of Anisozygoptera and Anisoptera, and to evaluate phylogenetic implications. Comparative analyses of the male vesica spermalis and the female ovipositor result in further hypotheses concerning the phylogenetic relationships of the subgroups of Anisoptera.