This paper examines the comovement of factors driving individual commodity futures curves. We adopt the framework of the global Nelson-Siegel model, which is a popular approach in modeling the term structure of interest rates in terms of level, slope and curvature factors. We extend the model by including a seasonal factor, to account for the fact that periodic behavior is an important feature of commodity futures prices. We put forward a model for the factor dynamics that allows for comovement across commodities by decomposing the factors into a global, sector and idiosyncratic component. Investigation of the loadings on these components shows that the level factors are mostly driven by a global level component, while the slope and curvature factors comove more due to common sector components. The advantage of our approach over existing price comovement literature is that by including cross-sectional information we can examine not only comovement in the price level of different commodities but also comovement in the slope or curvature of their curves, which can be linked to inventories via the Theory of Storage. One of our extensions allows for time-varying loadings and shows that comovement indeed varies over time. This time variation could be related to structural changes in the commodities futures market (e.g. the financialization of the commodities market).