The stability of magnetic fields in spherical
objects is studied, especially in the context
of neutron stars. Stability depends on both toroidal
and poloidal magnetic components, as well as on the
differential rotation. For that reason, we have
constructed a simulation in which an initial poloidal
field and differential rotation generate a toroidal
field consistently. At the same time, Lorentz forces
diminish the differential rotation. For any snap-shot
of this scenario, we ask for the stability against
non-axisymmetric perturbations and find severe
differences to earlier results for purely toroidal
fields.