This article addresses the issue of whether the remember-know (RK) task is best explained by a single-process or a dual-process model. All single-process models propose that remember and know responses reflect different levels of a single strength-of-evidence dimension. Thus, across conditions in which response criteria are held constant, these models predict that the RK task is unidimensional. Many dual-process models propose that remember and know responses reflect two qualitatively distinct processes underlying recognition memory, often characterized as recollection and familiarity. These models predict that the RK task is bidimensional. Using data from 37 studies, the author conducted a state-trace analysis to determine the dimensionality of the RK task. In those studies, non-memory-related differences between conditions were eliminated via decision criteria constrained to be constant across all levels of the independent variables. The results reveal little or no evidence of bidimensionality and lend additional support to the unequal-variance signal detection model. Other arguments supporting a bidimensional interpretation are examined, and the author concludes there is insufficient evidence for the RK task to be used to identify qualitatively different memory components.(PsycINFO Database Record (c) 2016 APA, all rights reserved)