Studies of saccadic suppression and induced motion have suggested separate representations of visual space for perception and visually guided behavior. Because these methods required stimulus motion, subjects might have confounded motion and position. We separated cognitive and sensorimotor maps without motion of target, background, or eye, with an "induced Roelofs effects": a target inside an off-center frame appears biased opposite the direction of the frame. A frame displayed to the left of a subject's center line, for example, will make a target inside the frame appear farther to the right than its actual position. The effect always influences perception, but in half of our subjects it did not influence pointing. Cognitive and sensorimotor maps interacted when the motor response was delayed; all subjects now showed a Roelofs effect for pointing, suggesting that the motor system was being fed from the biased cognitive map. A second experiment showed similar results when subjects made an open-ended cognitive response instead of a five-alternative forced choice. Experiment 3 showed that the results were not due to shifts in subjects' perception of the felt straight-ahead position. In Experiment 4, subjects pointed to the target and judged its location on the same trail. Both measures showed a Roelofs effect, indicating that each trial was treated as a single event and that the cognitive representation was accessed to localize this event in both response modes.