This article reports results from a longitudinal study investigating the effects of low-to-moderate prenatal and postnatal lead exposure on the cognitive development of children during the first 18 months of life. Study hypotheses are expressed as a sequence of linear models for the outcome variable adjusted score on the Bayley Scales of Mental Development (MDIA), as a function of cord blood-lead concentration, infant blood-lead concentration at semiannual examinations, and other characteristics of study participants. These models are fitted to MDIA measurements on three occasions for as many as 214 infants, first assuming an arbitrary multivariate covariance structure for the repeated measurements and then with covariance structure arising from a random-effects model for errors. Estimates of the effects of lead exposure are not sensitive to the assumed covariance structure. The article describes several approaches to residual analysis and outlier detection in the longitudinal setting. In particular, it shows how empirical Bayes residuals can be used to estimate the partial regression coefficient of covariates not included in the linear model. The major findings concerning the effect of lead exposure on cognitive development are (a) a clear association between cord blood-lead concentration and Bayley scores in the first 18 months of life, (b) no clear evidence of an effect of cumulative postnatal exposure, and (c) a tendency for children who had higher lead concentrations at 6 months of age to exhibit poorer performance at 18 months than children with low lead concentrations. These findings have implications for acceptable blood-lead concentrations in children and pregnant women.