This study examines the influence of spatial attention on the responses of neurons in the middle temporal visual area (MT or V5) of extrastriate cortex. Two monkeys were trained to perform a direction-discrimination task. On each trial, two apertures of random-dot stimuli appeared simultaneously at two spatially separated locations; the monkeys were required to discriminate the direction of stimulus motion at one location while ignoring the stimulus at the other location. After extensive training, we recorded the responses of MT neurons in two configurations: 1) Both apertures placed "within" the neuron's receptive field (RF) and 2) one aperture covering the RF while the other was presented at a "remote" location. For each unit we compared the responses to identical stimulus displays when the monkey was instructed to attend to one or the other aperture. The responses of MT neurons were 8.7% stronger, on average, when the monkey attended to the spatial location that contained motion in the "preferred" direction. Attentional effects were equal, on average, in the within RF and remote configurations. The attentional modulations began approximately 300 ms after stimulus onset, gradually increased throughout the trial, and peaked near stimulus offset. An analysis of the neuronal responses on error trials suggests that the monkeys failed to attend to the appropriate spatial location on these trials. The relatively weak attentional effects that we observed contrast strikingly with recent results of Treue and Maunsell, who demonstrated very strong attentional modulations (median effect >80%) in MT in a task that shares many features with ours. Our results suggest that spatial attention alone is not sufficient to induce strong attentional effects in MT even when two competing motion stimuli appear within the RF of the recorded neuron. The difference between our results and those of Treue and Maunsell suggests that the magnitude of the attentional effects in MT may depend critically on how attention is directed to a particular stimulus and on the precise demands of the task.