In recognition, remember-responses are understood to be based on recollection, and know-responses are understood to be based on familiarity. Two kinds of models have been proposed for the process by which recognition decisions are made. In single-process models, familiarity and recollection are integrated, and there is a single criterion for recognition. In dual-process models, familiarity and recollection are segregated, and there are separate criteria for remember and know-judgments. Recent process models can account for the distribution of remember and know-responses (under a range of different assumptions) but do not address the time course of the recognition process. Paradoxical findings, indicating that familiarity is available faster than recollection but remember-responses are on average faster than know-responses, cannot be convincingly explained by any existing dual-process model. We propose a new model that resolves this paradox by analyzing in detail the time course of recollection and familiarity. Know-responses based on the high familiarity of the test item are faster than remember-responses based on recollection. However, low-familiarity, low-recollection responses are slow and are also categorized by participants as know-responses. Hence, the average know-response time is slower than average remember-response time because know-responses include both fast high-familiarity responses and slow low-familiarity, low-recollection responses. A 12-parameter quantitative model that describes the relationship among the effects of confidence, accuracy, and remember and know categorization on accuracy and reaction time provided the best fit between expected reaction time and observed reaction time among the models tested. (PsycInfo Database Record (c) 2024 APA, all rights reserved).