A notion of equiaromaticity is defined: two polycyclic systems are equiaromatic if their rings can be put into one-to-one correspondence such that corresponding pi ring currents are equal. In conjugated-circuit models, amongst other families, all isomeric unbranched catafused benzenoids sharing the same sequence of straight-chain lengths are predicted to be equiaromatic. In particular, all fibonacenes with equal numbers of hexagonal rings, from zig-zag to helicenoid isomers, are equiaromatic according to all conjugated-circuit models. Test calculations with small fibonacenes indicate that equiaromaticity is retained as a qualitative trend in the simplest molecular-orbital treatment of induced current. (C) 2014 Elsevier B.V. All rights reserved.