Longitudinal data arise frequently in medical studies and it is a com-
mon practice to analyze such complex data with nonlinear mixed-e®ects (NLME)
models which enable us to account for between-subject and within-subject vari-
ations. To partially explain the variations, covariates are usually introduced to
these models. Some covariates, however, may be often measured with substantial
errors. It is often the case that model random error is assumed to be distributed
normally, but the normality assumption may not always give robust and reliable
results, particularly if the data exhibit skewness. Although there has been consid-
erable interest in accommodating either skewness or covariate measurement error
in the literature, there is relatively little work that considers both features simul-
taneously. In this article, our objectives are to address simultaneous impact of
skewness and covariate measurement error by jointly modeling the response and
covariate processes under a general framework of Bayesian semiparametric nonlin-
ear mixed-e®ects models. The method is illustrated in an AIDS data example to
compare potential models which have di®erent distributional speci¯cations. The
¯ndings from this study suggest that the models with a skew-normal distribution
may provide more reasonable results if the data exhibit skewness and/or have
measurement errors in covariates.