  Magnetorotational instability (MRI) has been suggested to lead a rapid growth
of the magnetic field in core collapse supernovae and produce departures from
spherical syymmetry that can be important in determining the explosion
mechanism. We address the problem of stability in differentially rotating
magnetized proto-neutron stars at the beginning of their evolution. Criteria
for MRI in proto-neutron stars are derived without simplying assumptions about
a weak magnetic field and are substantially different from the standard
condition. If the magnetic field is strong, MRI can occur only in the
neighbourhood of the region where the spherical radial component of the
magnetic field vanishes. The growth rate of MRI is relatively low except for
perturbations with very small scales which usually are not detected in
numerical simulations. We find that MRI in proto-neutron stars grows more
slowly than than the double diffusive instability analogous the
Goldreich-Schubert-Fricke instability in ordinary stars.
