Prospective memory requires forming an intention that cannot be completed at the present time, remembering that intention, and then recognizing the appropriate time to execute it. We review recent work in our laboratory that has revealed prospective memory-like patterns of performance in nonhuman primates. Rhesus monkeys and capuchin monkeys were given computerized tasks in which the monkeys either had to remember a future response they could not make immediately, or they sometimes saw a particular stimulus during an ongoing task they had to remember to later indicate seeing or not seeing. Most monkeys succeeded on these tasks and even anticipated the necessary responses. Chimpanzees also showed evidence of prospective memory. They appeared to form intentions about less valuable food items that they did not want immediately but would want later, and they responded at a later time when it was possible to obtain those items. Even when the response option was embedded within an ongoing task, the chimpanzees still showed some success in remembering to carry out the prospective intention. This research indicates that nonhuman primates form intentions for future responses, maintain those intentions during a delay, and execute them at an appropriate time.