Magnetically induced current density susceptibilities and ring-current strengths have been calculated for neutral and doubly charged persubstituted benzenes C6X6 and C6X6 2+ with X = F, Cl, Br, I, At, SeH, SeMe, TeH, TeMe, and SbH2. The current densities have been calculated using the gauge-including magnetically induced current (GIMIC) method, which has been interfaced to the Gaussian electronic structure code rendering current density calculations using effective core potentials (ECP) feasible. Relativistic effects on the ring-current strengths have been assessed by employing ECP calculations of the current densities. Comparison of the ring-current strengths obtained in calculations on C6At6 and C6At6 2+ using relativistic and non-relativistic ECPs show that scalar relativistic effects have only a small influence on the ring-current strengths. Comparisons of the ring-current strengths and ring-current profiles show that the C6I6 2+, C6At6 2+, C6(SeH)6 2+, C6(SeMe)6 2+, C6(TeH)6 2+, C6(TeMe)6 2+, and C6(SbH2)6 2+ dications are doubly aromatic sustaining spatially separated ring currents in the carbon ring and in the exterior of the molecule. The C6I6 + radical cation is also found to be doubly aromatic with a weaker ring current than obtained for the dication.