Magnetically induced current density susceptibilities and ring-current strengths have been calculated for neutral and doubly charged persubstituted benzenes CX and CX with X = F, Cl, Br, I, At, SeH, SeMe, TeH, TeMe, and SbH. 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 CAt and CAt 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 CI, CAt, C(SeH), C(SeMe), C(TeH), C(TeMe), and C(SbH) dications are doubly aromatic sustaining spatially separated ring currents in the carbon ring and in the exterior of the molecule. The CI radical cation is also found to be doubly aromatic with a weaker ring current than obtained for the dication.