Nonlinear mixed-effects models are models in which one or more coefficients of the growth model enter in a nonlinear manner, such as appearing in the exponent of the growth function. In their applications, the within-individual residuals are often assumed to be independent with constant variance across time, an assumption that implies that the assumed growth function fully accounts for the dependencies and patterns of variation in the data. Studies have shown that a poorly specified within-individual residual covariance structure of a linear mixed-effects model can impact the estimated covariance matrix of the random effects at the second-level, model fit and statistical inference. The consequences for nonlinear mixed-effects models are not, however, clearly understood. This is due in part to the differences in the estimation needs of the two types of models. Using empirical data examples, this work illustrates the impact of fitting alternative residual covariance structures in nonlinear mixed-effects models that do not entirely parallel the results from studies of strictly linear mixed-effects models and call for the need of researchers to consider alternative structures when fitting nonlinear mixed-effects models.