Infants born prematurely are at increased risk of adverse neurodevelopmental outcome. The measurement of white matter tissue composition and structure can help predict functional performance. Specifically, measurements of myelination and indicators of myelination status in the preterm brain could be predictive of later neurological outcome. Quantitative imaging of myelin could thus serve to develop biomarkers for prognosis or therapeutic intervention; however, accurate estimation of myelin content is difficult. This work combines diffusion MRI and multi-component T2 relaxation measurements in a group of 37 infants born very preterm and scanned between 27 and 58 weeks equivalent gestational age. Seven infants have longitudinal data at two time points that we analyze in detail. Our aim is to show that measurement of the myelin water fraction is achievable using widely available pulse sequences and state-of-the-art algorithmic modeling of the MR imaging procedure and that a multi-component fitting routine to multi-shell diffusion weighted data can show differences in neurite density and local spatial arrangement in grey and white matter. Inference on the myelin water fraction allows us to demonstrate that the change in diffusion properties of the preterm thalamus is not solely due to myelination (that increase in myelin content accounts for about a third of the observed changes) whilst the decrease in the posterior white matter T2 has no significant component that is due to myelin water content. This work applies multi-modal advanced quantitative neuroimaging to investigate changing tissue properties in the longitudinal setting. Hum Brain Mapp 37:2479–2492, 2016. © 2016 Wiley Periodicals, Inc.