We investigate a new type of structural instability of regular I-D molecular stacks consisting of homonuclear disc-like molecules, in particular of polycyclic aromatic hydrocarbons. If the repeating units are separated by mirror planes of symmetry, it is shown that the interaction energy of such systems is non-bonding, i.e., the ground state is unstable with regard to a distorsion which eliminates the symmetry plane. (C) 2003 Elsevier Science B.V. All rights reserved.