The paper deals with the problem of emergence of the most ancient burial mounds in the southern part of Eastern Europe. The author starts with discussing the most disputable issues related to the problem in question and compares different approaches to it. The period under consideration is divided into four main stages: Early, Middle and Late Eneolithic (c. 5000–3500 BC), and Early Bronze Age I (c. 3500–3000 BC). It is shown that there are no reliable grounds to date the emergence of the first kurgans to the Early Eneolithic. Moreover, even for the Middle Eneolithic evidence for the existence of true kurgans remains rather unconvincing. It is concluded that the most ancient kurgans in the East European steppes seem to have appeared as late as the beginning of the second quarter of the 4th millennium BC. This event was conditioned by a complex combination of social, economic, technological and environmental factors.