The nondipolar component of the geomagnetic field is likely to dominate during at least some geomagnetic reversals. The magnetosphere and auroral zones for a nondipolar field are more complex than for a dipole field. To begin to explore the nature of this complexity, we have studied the auroral zones appropriate to a pure quadrupole field. The quadrupole coefficients for the historical geomagnetic field were used in the study. The result is that such auroral zones are much more extensive than at present. They extend in association with two great circles from the tropics to midlatitudes in both north and south hemispheres. As a consequence, bombardment of the upper atmosphere by magnetosheath (polar cusp) and quasitrapped energetic magnetospheric (plasma sheet) particle is also much more extensive.