Huckel-London-Pople-McWeeny (HLPM) 'topological' ring-currents calculated for certain [N]-circulenes are in accord with (a) the previous generalised predictions based on the London approach and (b) the ab-initio ipso-centric pi-electron current-density maps that this series of conjugated structures does not conform to the 'annulene-within-an-annulene' (AWA) model. These considerations are extended beyond the [N]-circulenes to a series of structures formally related to kekulene. One such system studied, anti-kekulene, with a [4n]-perimeter (n = 6) and [4n]-central ring (n = 3), exhibits paramagnetic topological bond-currents in its periphery, and a mixture of both paramagnetic and diamagnetic bond-currents in its central (overall, paramagnetic) ring. (C) 2011 Elsevier B.V. All rights reserved.