Competition for attention between 2 written words was investigated by presenting the words briefly in a single stream of distractors (Experiment 1) or in different streams (Experiment 2-6), using rapid serial visual presentation at 53 ms/item. Stimulus onset asynchrony (SOA) was varied from 0 to 213 ms. At all SOAs there was strong competition, but which word was more likely to be reported shifted markedly with SOA. At SOAs in the range of 13-53 ms the second word was more likely to be reported, but at 213 ms, the advantage switched to the first word, as in the attentional blink. A 2-stage competition model of attention is proposed in which attention to a detected target is labile in Stage 1. Stage 1 ends when one target is identified, initiating a serial Stage 2 process of consolidation of that target.