Long document coreference resolution remains a challenging task due to the\nlarge memory and runtime requirements of current models. Recent work doing\nincremental coreference resolution using just the global representation of\nentities shows practical benefits but requires keeping all entities in memory,\nwhich can be impractical for long documents. We argue that keeping all entities\nin memory is unnecessary, and we propose a memory-augmented neural network that\ntracks only a small bounded number of entities at a time, thus guaranteeing a\nlinear runtime in length of document. We show that (a) the model remains\ncompetitive with models with high memory and computational requirements on\nOntoNotes and LitBank, and (b) the model learns an efficient memory management\nstrategy easily outperforming a rule-based strategy.\n