The nonlinear mixed effects model is used to represent data in pharmacokinetics, viral dynamics, and other areas where an objective is to elucidate associations among individual-specific model parameters and covariates; however, covariates may be measured with error. For additive measurement error, we show substitution of mismeasured covariates for true covariates may lead to biased estimators for fixed effects and random effects covariance parameters, while regression calibration may eliminate bias in fixed effects but fail to correct that in covariance parameters. We develop methods to take account of measurement error that correct this bias and may be implemented with standard software, and we demonstrate their utility via simulation and application to data from a study of HIV dynamics.