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Competition between memories can cause weakening of those memories. Here we investigated memory competition during sleep in human participants by presenting auditory cues that had been linked to two distinct picture-location pairs during wake. We manipulated competition during learning by requiring participants to rehearse picture-location pairs associated with the same sound either competitively (choosing to rehearse one over the other, leading to greater competition) or separately; we hypothesized that greater competition during learning would lead to greater competition when memories were cued during sleep. With separate-pair learning, we found that cueing benefited spatial retention. With competitive-pair learning, no benefit of cueing was observed on retention, but cueing impaired retention of well-learned pairs (where we expected strong competition). During sleep, post-cue beta power (16–30 Hz) indexed competition and predicted forgetting, whereas sigma power (11–16 Hz) predicted subsequent retention. Taken together, these findings show that competition between memories during learning can modulate how they are consolidated during sleep.