We consider dependent functional data that are correlated because of a longitudinal‐based design: each subject is observed at repeated times and at each time, a functional observation (curve) is recorded. We propose a novel parsimonious modelling framework for repeatedly observed functional observations that allows to extract low‐dimensional features. The proposed methodology accounts for the longitudinal design, is designed to study the dynamic behaviour of the underlying process, allows prediction of full future trajectory and is computationally fast. Theoretical properties of this framework are studied, and numerical investigations confirm excellent behaviour in finite samples. The proposed method is motivated by and applied to a diffusion tensor imaging study of multiple sclerosis. Copyright © 2015 John Wiley & Sons, Ltd.