Unusually well-preserved fossils of a Halicyne-like cycloid crustacean frequently occur in the early Late Triassic lacustrine clay bed at Krasiejów in Opole Silesia, southern Poland. Its gill-like structures form a horseshoe-shaped pair of units composed of numerous calcified blades with reverse U-shaped cross-section. Originally, these were parallel slits opening on the ventral surface of the carapace. Lobation of the posterior margin of the carapace, of unusually large mature size for the group, make the animal different from other members of Halicynidae, and the new name Opolanka decorosa gen. et sp. nov. is proposed for it. More completely preserved specimens of cycloids from Vosges, France, and Madagascar show that the slit openings were located above radially arranged coxae of the walking appendages and a reduced abdomen. The disposition and arrangement of the cycloid gills suggest at least close analogy, and possibly homology, with the "respiratory areas" of the Branchiura, serving mostly as ion-exchange organs. It is proposed that they originated, in connection with the body size increase and adaptation to fresh-water environment, as radially arranged infoldings of the respiratory areas cuticle, with strongly calcified rigid dorsal parts suspended from the carapace. At least three ecologically and anatomically distinct lineages were represented in the order Cyclida, which was probably initially confined to marine environments and gradually adapted to life in continental waters. New taxa Schraminidae fam. nov. (with Schramine gen. nov.) and Americlidae fam. nov. (with Americlus gen. nov.) are proposed.