In the more than 320 million years old evolution the monophyletic group Odonatoptera (dragonflies) developed a number of unique morphological adaptations. One of them is the very complex mating behaviour (,tandem position' and ,wheel position') which is the strongest argument for a monophyletic status of the recent dragonflies. A first theory concerning the development of this strange behaviour as well as the evolution of such unique structures was published by ZESSIN [1995]; it was modified subsequently by BECHLY, BRAUCKMANN, ZESSIN & GRONING [2001] and ZESSIN et al [2001]. Based upon two fossil specimens of Namurotypus sippeli Brauckmann & Zessin 1989 and Erasipteroides valentini (Brauckmann 1985) of Namurian B age from Hagen-Vorhalle, Germany, with preserved wings as well as even the male and female genitalia, the evolution of the, mating wheel' and of the mode of oviposition of recent dragonflies with its peculiar copulation apparatus is discussed; both specimens are therefore of outstanding scientific value for the reconstruction of the development of these body structures. The enlargement of the wing-span of certain Late Palaeozoic Odonatoptera [as for example the specimens mentioned above from the Namurian B of Hagen-Vorhalle; Erasipterella piesbergensis Brauckmann 1983, and Piesbergtupus hielscheri Zessin 2006 of Westphalian D age of the Piesberg near Osnabruck, Germany, and other Permocarboniferous species from Central Europe and North America] is discussed in connection with the supposed increasing oxygene concentration in the air during the Late Carboniferous and Early Permian; largest known insect at all is the Early Permian Meganeuropsis permiana Carpenter 1939 with a wing-span of 72 cm. The flying ability of the giant Odonatoptera is discussed, too, by focussing on Stephanotypus schneideri Zessin 1983. Gliding flight is assumed to be predominant, interrupted by phases of wing flapping. Improvements of the flight ability by nodus- and pterostigma-like structures within the wings were already developed during the Late Carboniferous. Certain characters of the head (size of mandibles and eyes) and spiniferous legs (with three terminal claws) recommend a predatory mode of life similar to the ones of recent Odonatoptera. The well-preserved large orthopteroid-like ovipositor of Erasipteroides valentini (Brauckmann 1985) suggests an endophytic or an endosubstratic oviposition in soils at the bottom of ponds. The giant dragonflies (Meganisoptera) were not able to adapt their mode of life to the rapidly decreasing oxygene concentration in the air at the end of the Permian period and became completely extinct. Other, smaller Permocarboniferous Odonatoptera with petiolate wing-base - for example such Protozygoptera as Bechlya ericrobinsoni Jarzembowski & Nel 2002, Oboraneura kukalovae Zessin 2008, the species of the Kennedyidae Tillyard 1925 and Saxonagrion minutus Nel et al 2000 (firstly grouped by NEL et al 2000 with the Zygoptera Selys 1854, then, NEL et al 2008, with the Panodonata) - survived the Permian/ Triassic crisis and gave origin to the rich diversity of the Mesozoic and to the recent species. The socalled,secondary copulation' must have already evolved during Permocarboniferous or Lower Triassic, because each of the recent suborders of the Odonata [Anisoptera, Anisozygoptera, and Zygoptera] share it; therefore their common stem species (presumably of Permian or Triassic age) must already have had ,secondary copulation' (with the female taking off the sperm from a special structure at the 2 nd and 3 rd abdominal segment while forming a,mating wheel' with the male). The larval instars of the giant Odonatoptera are poorly known; a single wing of a nymph is described from the Stephanian of Wettin (Sachsen-Anhalt, Germany) as Schlechtendaliola nympha Handlirsch 1919.