Populations of trapped particles in Earth's magnetic field are intimately linked to prominent magnetospheric phenomena, for example, to the radiation belts and the ring current. Particles are forced to bounce between both hemispheres because field lines converge from the magnetic equatorial region toward the poles owing to the dominating dipolar component. The scenario may change essentially if the so-called paleomagnetosphere is considered, that is, the terrestrial magnetosphere during a polarity reversal period. This report deals with particle trapping in general field configurations and concentrates on the quadrupole case as a potential scenario for paleomagnetospheric studies. By using the tensor representation of the quadrupole field, we show that its topology is controlled by a single shape parameter which is a measure for the relative strength of quadrupole tensor components, or equivalently, coefficients in the spherical harmonics expansion of the potential. In order to locate centers of particle bounce motion the concept of a magnetic equatorial surface is extended to a more general type of trapping center surface by means of geometrical criteria such as B⋅∇B=0. The quadrupole case yields two such surfaces. As does the field line topology, those surfaces and the resulting drift orbits vary strongly with the quadrupole shape parameter. ¿ 2000 American Geophysical Union