Driving on a busy road, eluding a group of predators, or playing a team sport involves keeping track of multiple moving objects. In typical laboratory tasks, the number of visual targets that humans can track is about four. Three types of theories have been advanced to explain this limit. The fixed-limit theory posits a set number of attentional pointers available to follow objects. Spatial interference theory proposes that when targets are near each other, their attentional spotlights mutually interfere. Resource theory asserts that a limited resource is divided among targets, and performance reflects the amount available per target. Utilising widely separated objects to avoid spatial interference, the present experiments validated the predictions of resource theory. The fastest target speed at which two targets could be tracked was much slower than the fastest speed at which one target could be tracked. This speed limit for tracking two targets was approximately that predicted if at high speeds, only a single target could be tracked. This result cannot be accommodated by the fixed-limit or interference theories. Evidently a fast target, if it moves fast enough, can exhaust attentional resources. (Contains 8 figures.)