Abstract This article presents an Analysis of Variance model for functional data that explicitly in- corporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour be etles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smootheness of the observed data is not required; the method can be applied to the sparsely observed data that is often encountered in longitudinal studies. Key words: Karhunen–Lo`eve decomposition; longitudinal data; phase variability; quan- titative genetics; random-effect models.