It has been suggested that, during tasks in which subjects are exposed to a visual rotation of cursor feedback, alternating bimanual adaptation to opposing rotations is as rapid as unimanual adaptation to a single rotation (Bock et al. in Exp Brain Res 162:513-519, 2005). However, that experiment did not test strict alternation of the limbs but short alternate blocks of trials. We have therefore tested adaptation under alternate left/right hand movement with opposing rotations. It was clear that the left and right hand, within the alternating conditions, learnt to adapt to the opposing displacements at a similar rate suggesting that two adaptive states were formed concurrently. We suggest that the separate limbs are used as contextual cues to switch between the relevant adaptive states. However, we found that during online correction the alternating conditions had a significantly slower rate of adaptation in comparison to the unimanual conditions. Control conditions indicate that the results are not directly due the alternation between limbs or to the constant switching of vision between the two eyes. The negative interference may originate from the requirement to dissociate the visual information of these two alternating displacements to allow online control of the two arms.