Was the spread of agro-pastoralism from the Eurasian founder regions dominated by demic or by cultural diffusion? This study employs simulations that unfold a complex inter-regional and time varying pattern of demic and diffusive exchange processes during the Neolithisation, and thus supports from a modelling perspective the hypothesis that there is no simple or exclusive demic or cultural diffusion, but that in most regions of Eurasia a combination of demic and cultural processes were important.