To grow straight and upright, plants need to regulate actively their posture. Gravitropic movement, which occurs when plants modify their growth and curvature to orient their aerial organ against the force of gravity, is a major feature of this postural control. A recent model has shown that graviception and proprioception are sufficient to account for the gravitropic movement and subsequent organ posture demonstrated by a range of species. However, some plants, including wheat coleoptiles, exhibit a stronger regulation of posture than predicted by the model. Here, we performed an extensive kinematics study on wheat coleoptiles during a gravitropic perturbation (tilting) experiment in order to better understand this unexpectedly strong regulation. Close temporal observations of the data revealed that both perturbed and unperturbed coleoptiles showed oscillatory pulses of elongation and curvature variation that propagated from the apex to the base of their aerial organs. In perturbed coleoptiles, we discovered a non-trivial coupling between the oscillatory dynamics of curvature and elongation. The relationship between those oscillations and the postural control of the organ remains unclear, but indicates the presence of a mechanism that is capable of affecting the relationship between elongation rate, differential growth, and curvature.