The study shows that differences in the level of inherited Neanderthal DNA between Europeans and East Asians cannot be explained by natural selection alone. Analysis of neutral regions of the genome allows us to reject the simple one-pulse model of gene flow. Instead, the data are best explained by a model that assumes two stages of interbreeding: the first before the separation of the ancestors of Europeans and East Asians, and the second after this separation, involving only the ancestors of Asians. Alternatively, a scenario of dilution of Neanderthal DNA in Europeans by admixture with a population that had no contact with Neanderthals (e.g., from Africa or the so-called "ghost population" in Eurasia) is also possible. However, to explain the data, such a contribution would have to be more than 18%, much higher than the known African admixture in Europe. Models accounting for two stages of interbreeding are therefore more likely. The study also confirms earlier estimates that the ancestors of Europeans had about 1.6-1.9 times the effective population size of the ancestors of Asians. Overall, the history of admixture between Homo sapiens and Neanderthals turns out to be more complex than previously thought and requires more sophisticated demographic models.