The hypothesis is tested whether the P1 of the event-related potential (ERP) component behaves like an evoked, traveling alpha wave. This hypothesis is based on different kinds of evidence showing, e.g., that-after undergoing phase reorganization-frequencies in the broad alpha range become synchronized (aligned) in absolute phase and contribute significantly to the generation of the P1. We investigated data from a Stroop task in which subjects had to respond only to the color and ignore the meaning of the presented words. Analyzing topographical phase relationships expressed in terms of traveling speed (with respect to Pz as trailing site) revealed that a systematic posterior to anterior traveling pattern appeared only in the broad time window of the P1-N1 complex and in the extended alpha frequency range. The obtained findings are consistent with the oscillatory ERP model and suggest that the P1 component may be considered a manifestation of an evoked, traveling alpha wave. We assume that the P1 reflects a top-down process in a sense that traveling alpha waves control or "gate" the direction of information processing in the brain.