An essential feature of intelligent sensory processing is the ability to focus on the part of the signal of interest against a background of distracting signals, and to be able to direct this focus at will. In this paper the problem of auditory streaming is considered and a model of the early stages of the process is proposed. The behavior of the model is shown to be in agreement with a number of well-known psychophysical results, including the relationship between presentation rate, frequency separation and streaming, the temporal development of streaming, and the effect of background organization on streaming. The principal contribution of this model is that it demonstrates how streaming might result from interactions between the tonotopic patterns of activity of incoming signals and traces of previous activity which feed back and influence the way in which subsequent signals are processed. The significance of these results for auditory scene analysis is considered and a framework for the integration of simultaneous and sequential grouping cues in the perception of auditory objects is proposed.