Based on new material from the Upper Triassic Nayband Formation of east-central Iran and on type material from the Alpine Triassic, the taxonomy of the cementing bivalve families Prospondylidae, Plicatulidae, Dimyidae and Ostreidae is examined and their phylogenetic relations are discussed. The Prospondylidae are characterized by the presence of an early pectiniform stage in their Palaeozoic genera which disappeared in most later forms due to ontogenetic pre-displacement of cementation. The Plicatulidae probably evolved from an ancestor within the Prospondylidae by the formation of strong crura, which allowed the reduction of the lateral part of the ligament. Their hinge was later modified by shifting resilifer and crura in a ventral direction and by forming a secondary ligament dorsally. The emended genera EoplicatulaPseudoplacunopsis represent different early stages of this development. The species Eoplicatula parvadehensis sp. nov. and Pseudoplacunopsis asymmetrica sp. nov. from the Nayband Formation are described. The shell of some early Ostreidae is characterized by the lack of structural chambers and by the presence of an originally aragonitic inner shell layer. For such forms, the new genus Umbrostrea is proposed, and the new species Umbrostrea emamiiUmbrostrea iranica are described. The available data on shell microstructure as well as most conchological characters do not support a close relationship between Ostreidae, Plicatulidae and Dimyidae.