Absence and presence have generally been discussed as two aspects of either a temporal or a spatial relationship. With an Arendtian notion of presence as the capacity to define space and to appear in front of others, this article explores undocumentedness as a condition of simultaneous presence and absence. Drawing on ethnographic fieldwork and interviews with undocumented persons in Sweden, it is argued that the undocumented spatiality is paradoxical and Möbius. This article shows how concealment, disguise, diffusion and appearance are key to the different manifestations of presence and absence in undocumented people’s lives. It also shows how undocumented persons, by using their politically absent yet physically present bodies as vehicles for practicing dissensus, can find possibilities for recognition and action in public space.