Efforts to draw inferences about species occurrence frequently account for false negatives, the common situation when individuals of a species are not detected even when a site is occupied. However, recent studies suggest the need to also deal with false positives, which occur when species are misidentified so that a species is recorded as detected when a site is unoccupied. Bias in estimators of occupancy, colonization, and extinction can be severe when false positives occur. Accordingly, we propose models that simultaneously account for both types of error. Our approach can be used to improve estimates of occupancy for study designs where a subset of detections is of a type or method for which false positives can be assumed to not occur. We illustrate properties of the estimators with simulations and data for three species of frogs. We show that models that account for possible misidentification have greater support (lower AIC for two species) and can yield substantially different occupancy estimates than those that do not. When the potential for misidentification exists, researchers should consider analytical techniques that can account for this source of error, such as those presented here.