International audience Since Radcliffe-Brown’s rejection of what he called conjectural history, and through this also refusing to engage with evolutionary theses in general and those in the domain of kinship in particular, only few anthropologists have ventured into the realm of reconstructing past forms of social organization and imagining possible scenarios of historical transformations. Ethnography became, explicitly or implicitly, the fixed location of an illusionary and fallaciously everlasting present. At the same time, archaeology, linguistics and genetics have made considerable progress in analysing and understanding sociocultural trajectories, as well as with respect to one of the most difficult questions of the social sciences: what have been the rationales that triggered processes of cultural and linguistic diversification. After introducing these problems, this paper aims to reconsider Australian Aboriginal kinship systems (and potentially beyond) suggesting distinguishing two modes of the pragmatics of sociality: territorialized systems and societies, and networked or expansionist systems and societies. These two modes reflect different means and ways to deal with what appears to be a shared structural constitutive (the brother-sister relationship), but also contribute to explain the historical diversification in other sociocultural domains, such as totemism, transmission and inheritance or personal and collective naming systems.