{Background}: Among the main data-analytical advances of recent decades are Latent Growth Models (LGM) and Multilevel Models (MLM) for the analysis of longitudinal data. {Objective}: We discuss the relative advantages and disadvantages of the two analytical methods and offer some practical guidelines concerning the choice between LGM and MLM based on (a) completeness and balance of the data, (b) theoretical functional form of change examined, (c) examination of the error structure, (d) theoretical relations among differential level effects and differential change effects, and (e) role of timeinvariant covariates. {Methods}: To discuss LGM and MLM, we provide illustrations from applications to the Berlin Aging Study (BASE) and the Swiss Interdisciplinary Longitudinal Study on the Oldest Old (SWILSO-O). {Results}: As predicted by two-component theories of lifespan cognition, performance on a vocabulary test (indicator of broad crystallized intelligence) did not decline over time, while scores on a digit letter test (indicator of broad fluid intelligence) decreased over 6 years. Differential level effects were obtained on both variables, while average and differential change effects were obtained only for the digit letter test. In a second set of analyses, we tested the error-free effect that a broad fluid intelligence indicator exerted on the latent yearly change in a broad crystallized intelligence indicator, and vice versa. In both data sets we obtained strong evidence for a more reliable effect of the fluid indicator on the change in the crystallized indicator. This evidence provided support for the dedifferentiation hypothesis of cognitive abilities in very old age. {Conclusions}: New insights into cognitive aging phenomena can be gained with proper applications of LGM and MLM. We posit that the choice between LGM and MLM and their specification rests on theoretical and empirical motives to be defined a priori.