This study examined whether objects are attended in serial or in parallel during a demanding visual search task. A component of the event-related potential waveform, the N2pc wave, was used as a continuous measure of the allocation of attention to possible targets in the search arrays. Experiment 1 demonstrated that the relative allocation of attention shifts rapidly, favoring one item and then another. In Experiment 2, a paradigm was used that made it possible to track the absolute allocation of attention to individual items. This experiment showed that attention was allocated to one object for 100-150 ms before attention began to be allocated to the next object. These findings support models of attention that posit serial processing in demanding visual search tasks.