We present a new modeling framework for recognition memory and repetition priming based on signal detection theory. We use this framework to specify and test the predictions of 4 models: (a) a single-system (SS) model, in which one continuous memory signal drives recognition and priming; (b) a multiple-systems-1 (MS1) model, in which completely independent memory signals (such as explicit and implicit memory) drive recognition and priming; (c) a multiple-systems-2 (MS2) model, in which there are also 2 memory signals, but some degree of dependence is allowed between these 2 signals (and this model subsumes the SS and MS1 models as special cases); and (d) a dual-process signal detection (DPSD1) model, 1 possible extension of a dual-process theory of recognition (Yonelinas, 1994) to priming, in which a signal detection model is augmented by an independent recollection process. The predictions of the models are tested in a continuous-identification-with-recognition paradigm in both normal adults (Experiments 1-3) and amnesic individuals (using data from Conroy, Hopkins, & Squire, 2005). The SS model predicted numerous results in advance. These were not predicted by the MS1 model, though could be accommodated by the more flexible MS2 model. Importantly, measures of overall model fit favored the SS model over the others. These results illustrate a new, formal approach to testing theories of explicit and implicit memory.