  The magnetorotational instability (MRI) of differential rotation under the
simultaneous presence of axial and azimuthal components of the (current-free)
magnetic field is considered. For rotation with uniform specific angular
momentum the MHD equations for axisymmetric perturbations are solved in a local
short-wave approximation. All the solutions are overstable for B_z \cdot B_\phi
\neq 0 with eigenfrequencies approaching the viscous frequency. For more flat
rotation laws the results of the local approximation do not comply with the
results of a global calculation of the MHD instability of Taylor-Couette flows
between rotating cylinders. -- With B_phi and B_z of the same order the
traveling-mode solutions are also prefered for flat rotation laws such as the
quasi-Kepler rotation. For magnetic Prandtl number Pm\to 0 they scale with the
Reynolds number of rotation rather than with the magnetic Reynolds number (as
for standard MRI) so that they can easily be realized in MHD laboratory
experiments. -- Regarding the nonaxisymmetric modes one finds a remarkable
influence of the ratio B_\phi /B_z only for the extrema. For B_\phi >> B_z and
for not too small Pm the nonaxisymmetric modes dominate the traveling
axisymmetric modes. For standard MRI with B_z >> B_\phi, however, the critical
Reynolds numbers of the nonaxisymmetric modes exceed the values for the
axisymmetric modes by many orders so that they are never prefered.
