Observers made temporal order judgements (TOJs) regarding which of two tactile stimuli presented to either hand (at stimulus onset asynchronies of up to 200 ms) occurred first. When the observers' hands were placed in an uncrossed posture (i.e., each hand in its own hemispace), performance was accurate, with a just noticeable difference (JND; the smallest interval which produces 75% correct performance) of 34 ms. By contrast, when the hands were crossed over the midline, performance declined such that 124 ms was needed for accurate performance. In a second experiment, we presented visual instead of tactile stimuli to evaluate the relative contribution of motor and perceptual confusions to the effect. While performance with crossed hands was significantly worse than with uncrossed hands (JND=36 vs. 31 ms, respectively), this difference was negligible compared to that with tactile stimuli. In a third experiment, experienced observers showed a robust crossed-hands deficit which was not improved by using different fingers on either hand. We argue that the decline in tactile discrimination performance when the hands are crossed reflects a failure to represent appropriately near simultaneous bimanual tactile stimuli, and stands in marked contrast to many recent observations of efficient remapping of singly-presented tactile stimuli.