We report quantum chemistry investigations of the magnetic response of large polycyclic hydrocarbons to a high magnetic field. In strong fields the magnetisation vs. field of nanosize molecules becomes strongly non-monotonic. For nanographenes containing thousands of atoms this effect develops at ca. 10(1)-10(2) T. It is related to the motion of vortices in the frontier molecular orbitals and transformations of ring current patterns. The described phenomenon is general, in principle observable in all conjugated planar nanosize molecules. (c) 2006 Elsevier B.V. All rights reserved.