A model for analysing longitudinal growth data with covariates is proposed. It assumes that the data for each individual follow a nonlinear growth model, with parameters unique to that individual. The parameters of individuals are assumed to vary in the population, with the population mean of each parameter dependent upon covariates. Several simple, two-stage methods of estimation are described and compared for making inferences about the effects of covariates upon growth. We also present a method of model validation for nonlinear models. These two-stage methods solve the inference problem we encounter when performing multiple cross-sectional analyses of the effects of covariates along the age scale. In addition, these two-stage methods permit us to study the effects of covariates upon growth rate, or other, possibly nonlinear, growth parameters. We find that some methods are better than others at reproducing the covariate effects observed in a series of age-specific analyses of the data.