  We present numerical simulations of a self-sustaining magnetic field in a
differentially rotating non-convective stellar interior. A weak initial field
is wound up by the differential rotation; the resulting azimuthal field becomes
unstable and produces a new meridional field component, which is then wound up
anew, thus completing the `dynamo loop'. This effect is observed both with and
without a stable stratification. A self-sustained field is actually obtained
more easily in the presence of a stable stratification. The results confirm the
analytical expectations of the role of Tayler instability.
