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 ( 0.25 r _ { 200 } ) of haloes with virial masses \sim 6 \times 10 ^ { 13 } ( \sim 7 \times 10 ^ { 11 } ) h ^ { -1 } M _ { \odot } 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 that 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 .