Metacognition is the ability to monitor and control one's cognition. Monitoring may involve either public cues or introspection of private cognitive states. We tested rhesus monkeys (Macaca mulatta) in a series of generalization tests to determine which type of cues control metacognition. In Experiment 1, monkeys learned a perceptual discrimination in which a "decline-test" response allowed them to avoid tests and receive a guaranteed small reward. Monkeys declined more difficult than easy tests. In Experiments 2-4, we evaluated whether monkeys generalized this metacognitive responding to new perceptual tests. Monkeys showed a trend toward generalization in Experiments 2 & 3, and reliable generalization in Experiment 4. In Experiments 5 & 6, we presented the decline-test response in a delayed matching-to-sample task. Memory tests differed from perceptual tests in that the appearance of the test display could not control metacognitive responding. In Experiment 6, monkeys made prospective metamemory judgments before seeing the tests. Generalization across perceptual tests with different visual properties and mixed generalization from perceptual to memory tests provide provisional evidence that domain-general, private cues controlled metacognition in some monkeys. We observed individual differences in generalization, suggesting that monkeys differ in use of public and private metacognitive cues.