We studied the instability of a dissipative quasi-Keplerian flow influenced by a homogeneous axial magnetic field in the geometry of a Taylor-Couette system. Especially we focus on the excitation of nonaxisymmetric modes and the resulting angular momentum transport, not on dynamo action. The excitation of nonaxisymmetric modes requires higher rotation rates than the excitation of the axisymmetric mode and this the more the higher the azimuthal mode number?m?is. We find that the weak-field branch in the instability map of the nonaxisymmetric modes always has a positive slope (in?contrast to the axisymmetric modes) so that for given magnetic field the modes with m?>?0 always have an upper limit of the supercritical Reynolds number. To?excite a nonaxisymmetric mode at 1?AU in a Kepler disk, a?minimum field strength of about 1?Gauss is necessary. For weaker magnetic field the nonaxisymmetric modes decay. The angular momentum transport of the nonaxisymmetric modes is always positive and depends linearly on the Lundquist number of the background field. The molecular viscosity and the basic rotation rate do not influence the related α-parameter. We did not find any indication that the magnetorotational instability decays for small magnetic Prandtl numbers as was found by using shearing-box codes. At?1?AU in a Kepler disk and with a field strength of about?1?Gauss α proves to be (only) about?0.005.
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