In spoken interactions, interlocutors carefully plan and time their utterances, minimising gaps and overlaps between consecutive turns. Cross-linguistic comparison has indicated that spoken languages vary only minimally in terms of turn-timing, and language acquisition research has shown pre-linguistic vocal turn-taking in the first half year of life. These observations suggest that the turn-taking system may provide a fundamental basis for our linguistic capacities. The question remains however to what extent our capacity for rapid turn-taking is determined by modality constraints. The avoidance of overlapping turns could be motivated by the difficulty of hearing and speaking at the same time. If so, turn-taking in sign might show greater toleration for overlap. Alternatively, signed conversations may show a similar distribution of turn-timing as spoken languages, thus avoiding both gaps and overlaps. To address this question we look at turn-timing in question-answer sequences in spontaneous conversations of Sign Language of the Netherlands. The findings indicate that although there is considerable overlap in two or more signers when proper allowance is made for onset preparation, post-utterance retraction and the intentional holding of signs for response, turn-taking latencies in sign look remarkably like those reported for spoken language. This is consistent with the possibility that, at least with regard to responses to questions, speakers and signers follow similar time courses in planning and producing their utterances in on-going conversation. This suggests that turn-taking systems may well be a shared cognitive infrastructure underlying all modern human languages, both spoken and signed.