Neurons in cortical area MT have localized receptive fields (RF) representing the contralateral hemifield and play an important role in processing visual motion. We recorded the activity of these neurons during a behavioral task in which two monkeys were required to discriminate and remember visual motion presented in the ipsilateral hemifield. During the task the monkeys viewed two stimuli, sample and test, separated by a brief delay and reported whether they contained motion in the same or in opposite directions. 50-70% of MT neurons were activated by the motion stimuli presented in the ipsilateral hemifield, at locations far removed from their classical receptive fields. These responses were in the form of excitation or suppression and were delayed relative to conventional MT responses. Both excitatory and suppressive responses were direction selective but the nature and the timecourse of their directionality differed from the conventional excitatory responses recorded with stimuli in the RF. Direction selectivity of the excitatory remote response was transient and early, while the suppressive response developed later and persisted after stimulus offset. The presence or absence of these unusual responses on error trials, as well as their magnitude, was affected by the behavioral significance of stimuli used in the task. We hypothesize that these responses represent top-down signals from brain region(s) accessing information about stimuli in the entire visual field and about the behavioral state of the animal. The recruitment of neurons in the opposite hemisphere during processing of behaviorally relevant visual signals reveals a mechanism by which sensory processing can be affected by cognitive task demands.