The hypothesis that both genetic and linguistic similarities among Eurasian and North African populations are due to demic diffusion of neolithic farmers is tested against a wide database of allele frequencies. Demic diffusion of farming and languages from the Near East should have determined clines in areas defined by linguistic criteria; the alternative hypothesis of cultural transmission does not predict clines. Spatial autocorrelation analysis shows significant gradients in three of the four linguistic families supposedly affected by neolithic demic diffusion; the Afroasiatic family is the exception. Many such gradients are not observed when populations are jointly analyzed, regardless of linguistic classification. This is incompatible with the hypothesis that major cultural transformations in Eurasia (diffusion of related languages and spread of agriculture) took place without major demographic changes. The model of demic diffusion seems therefore to provide a mechanism explaining coevolution of linguistic and biological traits in much of the Old World. Archaeological, linguistic, and genetic evidence agree in suggesting a multidirectional process of gene flow from the Near East in the neolithic. However, the possibility should be envisaged that some allele frequency patterns can predate the neolithic and depend on the initial spread of Homo sapiens sapiens from Africa into Eurasia.