There still is no general agreement on the origins of the European gene pool, even though Europe has been more thoroughly investigated than any other continent. In particular, there is continuing controversy about the relative contributions of European Palaeolithic hunter-gatherers and of migrant Near Eastern Neolithic farmers, who brought agriculture to Europe. Here, we apply a statistical framework that we have developed to obtain direct estimates of the contribution of these two groups at the time they met. We analyze a large dataset of 22 binary markers from the non-recombining region of the Y chromosome (NRY), by using a genealogical likelihood-based approach. The results reveal a significantly larger genetic contribution from Neolithic farmers than did previous indirect approaches based on the distribution of haplotypes selected by using post hoc criteria. We detect a significant decrease in admixture across the entire range between the Near East and Western Europe. We also argue that local hunter-gatherers contributed less than 30% in the original settlements. This finding leads us to reject a predominantly cultural transmission of agriculture. Instead, we argue that the demic diffusion model introduced by Ammerman and Cavalli-Sforza [Ammerman, A. J. & Cavalli-Sforza, L. L. (1984) The Neolithic Transition and the Genetics of Populations in Europe (Princeton Univ. Press, Princeton)] captures the major features of this dramatic episode in European prehistory.