The relationships between hit, remember, and false alarm rates were examined across individual subjects in three remember-know experiments in order to determine whether signal detection theory would be consistent with the observed data. The experimental data differed from signal detection predictions in two critical ways. First, remember reports were unrelated, or slightly negatively related, to the commission of false alarms. Second, both response types (remembers and false alarms) were uniquely related to hit rates, which demonstrated that the hit rate cannot be viewed as the result of a single underlying strength process. These results are consistent with the dual-process signal detection model of Yonelinas (1994), in which performance is determined by two independent processes - retrieval of categorical context information (remembering) and discriminations based on continuous item strength. Remember and false alarm rates selectively tap these processes, whereas the hit rate is jointly determined. Monte Carlo simulations in which the dual-process model was used successfully reproduced the pattern in the experimental data, whereas simulations in which a signal detection model, with separate "old" and "remember" criteria, was used, did not. The results demonstrate the utility of examining individual differences in response types when one is evaluating memory models.