Accelerated longitudinal designs (ALDs) allow examining developmental changes over a period of time longer than the duration of the study. In ALDs, participants enter the study at different ages (i.e., different cohorts), and provide measures during a time frame shorter than the total study. They key assumption is that participants from the different cohorts come from the same population and, therefore, can be assumed to share the same general trajectory. The consequences of not meeting that assumption have not been examined systematically. In this article, we propose an approach to detect and control for cohort differences in ALDs using latent change score models in both discrete and continuous time. We evaluated the effectiveness of such a method through a Monte Carlo study. Our results indicate that, in a broad set of empirically relevant conditions, both latent change score (LCS) specifications can adequately estimate cohort effects ranging from very small to very large, with slightly better performance of the continuous-time version. Across all conditions, cohort effects on the asymptotic level (dAs) caused much larger bias than on the latent initial level (d₀). When cohort differences were present, including them in the model led to unbiased estimates. In contrast, not including them led to tenable results only when such differences were not large (d₀ ≤ 1 and dAs ≤ .2). Among the sampling schedules evaluated, those including at least three measurements per participant over 4 years or more led to the best performance. Based on our findings, we offer recommendations regarding study designs and data analysis. (PsycInfo Database Record (c) 2023 APA, all rights reserved).