Despite the recent renewal of indigenous models for the Neolithisation of Greece, this paper will go back to more old-fashioned models, and argue in favour of colonisation processes by small, maritime, pioneer groups that later interacted with local populations. This argumentation rests first on an analysis of the presently available data on the Mesolithic, which shows that none of the prerequisites of a local process is met. Second, it rests on the consideration of often-neglected aspects, such as the theoretical and practical knowledge implied by the adoption of agriculture together with the adoption of new crafts and architectural techniques. Third, it rests in the need to explain the random, but strong parallels between the Near-Eastern and Greek Neolithic.