Disasters or catastrophes engender social and spatial disorganization of the territories affected by these events and specific human behaviour. In this paper, we look both at the responses of societies in terms of specific human behaviour in times of disaster or catastrophe, which may be either a form of vulnerability or on the contrary of social resilience, and at the forms of emergence associated with such exceptional events. The first part proposes a typology of behaviours observed at times of catastrophe and identifies properties common to all such behaviours. Parts two and three ask whether behaviours observed at times of disaster or catastrophe (behaviours that stand apart from everyday behaviours and that can be observed both individually and collectively) can be characterized as emergent behaviours. Answering this involves weighing up inputs from the science of risk and the science of complexity. We present the different properties for characterizing emergent human behaviour, in order to recombine the disciplinary approach of scientific communities. This knowledge of the conditions underlying the emergence of behaviours points the way to how the phenomenon might be modelled.