We analysed the interactions and aromaticity electron-density delocalisation observed in π-π complexes between the phenalenyl radical and acenaphthylene, and the DNA and RNA nucleobases (adenine, guanine, cytosine, thymine and uracil). Interaction energies are obtained at the M06-2X/6-311++G(2df,p) computational level for gas phase and PCM-water conditions. For both the phenalenyl radical and acenaphthylene, the complexes formed with guanine are the most stable ones. Atoms in molecules and natural bond orbital results reveal weak π-π interactions between both interacting moieties, characterized by bond critical points between C⋅⋅⋅C and C⋅⋅⋅N atoms. Nucleus independent chemical shifts (NICS) indicate the retention of the aromatic character of the monomers in the outer region of the complex. The fluctuation indexes reveal a loss of electron delocalisation upon complexation for all cases except guanine complexes. Nevertheless, the interface region shows large negative NICS values, which is not associated with an increase of the aromaticity or electron-density delocalisation, but with magnetic couplings of both molecules, leading to an unrealistic description of the aromatic behaviour in that region.