This paper considers estimation of nonparametric components in a time-varying coefficient model with repeated measurements of responses and covariates. The responses are modeled as depending linearly on the covariates, with coefficients that are functions of time. The measurements are assumed to be independent for different subjects but can be correlated in an unspecified way at different time points within each subject.Three nonparametric estimates, namely kernel, smoothing spline and locally weighted polynomial, of the time-varying coefficients are derived for such repeatedly measured data. A cross-validation criterion is proposed for the selection of the corresponding smoothing parameters. Asymptotic properties, such as consistency, rates of convergence and asymptotic mean squared errors, are established for the kernel estimates. An example of predicting the growth of children born to HIV infected mothers based on gender, HIV status and maternal vitamin A levels shows that this model and the corresponding nonparametric estimates are useful in epidemiological studies.