The diural caudal skeleton of teleostean actinopterygians develops phylogeneticaily and ontogenetically from a polyural skeleton. The reduction of the polyural anlage to four, three, two or fewer centra in the adult caudal skeleton takes different pathways in different genera (e.g. compare Elops and Albula) and groups of teleosts. As a result, ural centra are not homologous throughout the teleosts. By numbering the ural centra in a homocercal tail in polyural fashion, one can demonstrate these and the following differences. The ventral elements (hypurals) always occur in sequential series, whereas the dorsal elements (epurals and uroneurals) may alter like the ural centra. The number of epurals, five or four in fossil primitive teleosts, is reduced in other primitive and advanced teleosts, but the same epurals are not always lost. The number of uroneurals, seven in fossil teleosts, is reduced in living teleosts, but it has not been demonstrated that the first uroneural is always derived from the neural arch of the same ural centrum. The landmark in the homocercal tail is the preural centrum I which can be identified by (1) bifurcation of the caudal artery and vein in its ventral element, the parhypural, (2) its position directly caudal to the preural centrum (PU2) which supports the lowermost principal caudal ray with its haemal spine, (3) carrying the third hypaxial element ventral to the course of arteria and vena pinnalis, and (4) by carrying the first haemal spine (parhypural) below the dorsal end of the ventral cartilage plate. The study of the development of the vertebral column reveals that teleosts have different patterns of centrum formation. A vertebral centrum is a complete or partial ring of mineralized, cartilaginous or bony material surrounding at least the lateral sides of the notochord. A vertebral centrum may be formed by arcocentrum alone, or arcocentral arcualia and chordacentrum, or arco-, chorda- and autocentrum, or arcocentral arcualia and autocentrum. This preliminary research demonstrates that a detailed ontogenetic interpretation of the vertebral centra and of the caudal skeleton of different teleosts may be useful tools for further interpretations of teleostean interrelationships.