Abstract In catacondensed hexagonal systems, a set of pair-wise resonant hexagons is resonant [Croat. Chem. Acta 56 (1983) 365], [J. Mol. Struct. (Theochem) 279 (1993) 41]. The first proof of this result was given by Hansen and Zheng [J. Mol. Struct. (Theochem) 279 (1993) 41]. Here we offer an alternative proof.