Ab initio pi-electron first-order current density maps and all-electron second-order magnetic properties, calculated at an uncorrelated level of theory by means of distributed-gauge methods, are presented for a series of neutral and dianionic fused tetracycles which can be regarded formally as perturbed annulenes. The reliability of the current density maps, which point to the naphthalene core rather than the annulene perimeter as the basic unit of current flow, is supported by the good agreement of the computed magnetic properties with the available experimental data. Unusually for a closed-shell system, the acepleiadylene dianion is predicted to be a paramagnetic molecule.