Finite-field calculations of non-linear induced current density in representative [4n + 2] and [4n] pi systems, benzene and flat cyclo-octatetraene (COT), show that a strong uniform perpendicular magnetic field enhances benzene pi-diatropicity and decreases COT pi-paratropicity. The non-linear current is stronger by two orders of magnitude in COT, but still small: at 1a(0) height and in a field of 25 T. third-order effects contribute -5 ppm to the first-order pi ring current. Classical arguments based on radial contraction of charge density rationalise the non-linear response of benzene, but that of COT depends on a specific orbital-rotation effect, characteristic of paratropic pi systems. (C) 2004 Elsevier B.V. All rights reserved.