  The linear marginal instability of an MHD Taylor-Couette flow of infinite
vertical extension is considered. For hydrodynamically unstable flows the
minimum Reynolds number exists even without a magnetic field, but there are
also solutions with smaller Reynolds numbers for certain (weak) magnetic
fields. The magnetic field can, therefore, destabilize the rotating flow. This
instability, however, can only exist for not too small magnetic Prandtl
numbers. Also the situation for nonaxisymmetric disturbances is considered.
Without magnetic fields such modes possess higher Reynolds numbers than the
axisymmetric modes. The situation is changed in the MHD regime. For modest
magnetic fields the excitation of modes with m=1 is easier than the excitation
of modes with m=0 if critical magnetic amplitudes are exceeded.
