Edge-assignment determines the perception of relative depth across an edge and the shape of the closer side. Many cues determine edge-assignment, but relatively little is known about the neural mechanisms involved in combining these cues. Here, we manipulated extremal edge and attention cues to bias edge-assignment such that these two cues either cooperated or competed. To index their neural representations, we flickered figure and ground regions at different frequencies and measured the corresponding steady-state visual-evoked potentials (SSVEPs). Figural regions had stronger SSVEP responses than ground regions, independent of whether they were attended or unattended. In addition, competition and cooperation between the two edge-assignment cues significantly affected the temporal dynamics of edge-assignment processes. The figural SSVEP response peaked earlier when the cues causing it cooperated than when they competed, but sustained edge-assignment effects were equivalent for cooperating and competing cues, consistent with a winner-take-all outcome. These results provide physiological evidence that figure-ground organization involves competitive processes that can affect the latency of figural assignment.