Aims. We study the distribution of nearby thick-disc and halo stars in subspaces defined by their characteristic orbital parameters. Our aim is to establish the origin of the structure reported in particular in the Rmax − zmax space. Methods. To this end, we computed the orbital parameters and frequencies of stars for a generic and for a Stäckel Milky Way potential. Results. We find that for both the thick-disc and halo populations, very similar prominent substructures are apparent for the generic Galactic potential, while no substructure is seen for the Stäckel model. This indicates that the origin of these features is not merger-related, but due to the non-integrability of the generic potential. This conclusion is strengthened by our frequency analysis of the orbits of stars, which reveals the presence of prominent resonances, with ∼30% of the halo stars associated with resonance families. In fact, the stars in resonances define the substructures seen in the spaces of characteristic orbital parameters. Intriguingly, we find that some stars in our sample and in debris streams are on the same resonance as the Sagittarius dwarf. Conclusions. Our study constitutes a step towards disentangling the imprint of merger debris from substructures driven by internal dynamics. Given their prominence, these resonant-driven overdensities could potentially be useful in constraining the exact form of the Galactic potential.