One influential model of recognition posits two underlying memory processes: recollection, which is detailed but relatively slow, and familiarity, which is quick but lacks detail. Most of the evidence for this dual-process model in nonhumans has come from analyses of receiver operating characteristic (ROC) curves in rats, but whether ROC analyses can demonstrate dual processes has been repeatedly challenged. Here, we present independent converging evidence for the dual-process model from analyses of recognition errors made by rhesus monkeys. Recognition choices were made in three different ways depending on processing duration. Short-latency errors were disproportionately false alarms to familiar lures, suggesting control by familiarity. Medium-latency responses were less likely to be false alarms and were more accurate, suggesting onset of a recollective process that could correctly reject familiar lures. Long-latency responses were guesses. A response deadline increased false alarms, suggesting that limiting processing time weakened the contribution of recollection and strengthened the contribution of familiarity. Together, these findings suggest fast familiarity and slow recollection in monkeys, that monkeys use a "recollect to reject" strategy to countermand false familiarity, and that primate recognition performance is well-characterized by a dual-process model consisting of recollection and familiarity.