Edmund (1960) has shown that in the dentitions of almost all non-mammalian vertebrates, teeth are replaced in waves which regularly sweep through alternate tooth positions. He explained the ontogeny of these patterns of tooth replacement in terms of biological units called Zahnreihen whose existence has been accepted by nearly all workers studying tooth replacement. In the present paper it is argued that there is no unequivocal evidence, either during development or in adult animals, that Zahnreihen have any biological significance. Reconstructions were made from serial sections of the developing dentitions in the lower jaws of 15 embryos of Lacerta vivipara. It was evident that Zahnreihen have no significance in this animal. Rudimentary teeth were produced with varying frequency in positions 3, 5, 6, 8, 10 and 13. Contrary to the predictions of all previous theories explaining the ontogeny of tooth development in reptiles it was in these apparently random positions that the first teeth were produced. Furthermore, apart from during the first few days of embryonic dental development, it was clear that the development of a row of alternating teeth was initiated in sequence from the back to the front of the jaw to be followed by a similar sequence of development of the intervening teeth. On the basis of this evidence a new model to explain the sequence of tooth initiation in reptiles is proposed. The following assumptions have been made. (A) Ectomesenchymal cells migrate anteriorly through the developing jaws initiating a reaction from the oral ectoderm. (B) The oral ectoderm develops competence to react to the ectomesenchyme in three stages. First it generates abortive clumps of ectodermal cells; second it becomes capable of inducing the adjacent ectomesenchymal cells to form dentine and third it becomes capable of laying down enamel. (C) At all times the dental lamina has the potential of taking part in tooth development according to the regional competence achieved. (D) Developing tooth germs produce a condition which inhibits tooth development around them. Using these assumptions it is possible to explain all stages in the development of the wave replacement of alternate teeth in L. vivipara. It is also possible to explain previous observations on the ontogeny of reptilian dentitions. The sphere of inhibition which surrounds developing teeth is particularly important because it ensures that developing teeth are evenly spaced through the jaw. It is argued that the wave replacement of alternate teeth is an automatic sequel to this and is of only secondary functional significance.