The Neolithic transition in west Eurasia occurred in two main steps: the gradual development of sedentism and plant cultivation in the Near East and the subsequent spread of Neolithic cultures into the Aegean and across Europe after 7000 cal BCE. Here, we use published ancient genomes to investigate gene flow events in west Eurasia during the Neolithic transition. We confirm that the Early Neolithic central Anatolians in the ninth millennium BCE were probably descendants of local hunter-gatherers, rather than immigrants from the Levant or Iran. We further study the emergence of post-7000 cal BCE north Aegean Neolithic communities. Although Aegean farmers have frequently been assumed to be colonists originating from either central Anatolia or from the Levant, our findings raise alternative possibilities: north Aegean Neolithic populations may have been the product of multiple westward migrations, including south Anatolian emigrants, or they may have been descendants of local Aegean Mesolithic groups who adopted farming. These scenarios are consistent with the diversity of material cultures among Aegean Neolithic communities and the inheritance of local forager know-how. The demographic and cultural dynamics behind the earliest spread of Neolithic culture in the Aegean could therefore be distinct from the subsequent Neolithization of mainland Europe.