We explore the dynamical signatures imprinted by baryons on dark matter haloes during the formation process using the OverWhelmingly Large Simulations (OWLS), a set of state-of-the-art high-resolution cosmological hydrodynamical simulations. We present a detailed study of the effects of the implemented feedback prescriptions on the orbits of dark matter particles, stellar particles and subhaloes, analysing runs with no feedback, with stellar feedback and with feedback from supermassive black holes. We focus on the central regions (0.25r200) of haloes with virial masses ˜6 × 1013 (˜7 × 1011) h-1 M⊙ at z= 0 (2). We also investigate how the orbital content (relative fractions of the different orbital types) of these haloes depends on several key parameters such as their mass, redshift and dynamical state. The results of spectral analyses of the orbital content of these simulations are compared, and the change in fraction of box, tube and irregular orbits is quantified. Box orbits are found to dominate the orbital structure of dark matter haloes in cosmological simulations. There is a strong anticorrelation between the fraction of box orbits and the central baryon fraction. While radiative cooling acts to reduce the fraction of box orbits, strong feedback implementations result in a similar orbital distribution to that of the dark matter only case. The orbital content described by the stellar particles is found to be remarkably similar to that drawn from the orbits of dark matter particles, suggesting that either they have forgotten their dynamical history, or subhaloes bringing in stars are not biased significantly with respect to the main distribution. The orbital content of the subhaloes is in broad agreement with that seen in the outer regions of the particle distributions.