This paper considers the analysis of serial data on the growth of tumours in laboratory rodents. I propose a model-a generalization of the tumour growth model of Norton and Simon-that leads to a rich family of growth and decay curves. The model assumes that unperturbed growth follows the generalized logistic form; it accommodates time-varying treatment effects through an effective dose function. I fit two such models to data on a human prostate tumour growing in nude mice and compare the fitted curves and dose functions with a non-parametric curve and dose function estimated from a cubic spline model. All three models account for both random animal effects and autocorrelation. Monte Carlo results suggest that (a) maximum likelihood estimates of growth parameters are biased, although not severely, and (b) standard errors are conservative in small samples but become increasingly accurate in larger samples.