The theory of magnetoionic mode coupling is extended to the case in which the superposed magnetic field varies in amplitude and direction. Calculations are limited to the case X, Y, Z « 1 and to the case of a medium stratified in planes parallel to the wave front. In the quasi-longitudinal (QL) case, there is a "transitional" frequency, ft, such that, when f «ft, the modes are weakly coupled and the ordinary magnetoionic theory prevails; when J «f , there is strong coupling, and the wave propagates as if the magnetic field were absent. The QL transitional frequency is given by ft = 3 X 10- NS, where N is electron density (cm i) and S is the scale of the magnetic field (cm). In the ionosphere and in interplanetary and interstellar regions, ft is estimated to be cps; thus the magnetoionic modes at radio frequencies are always weakly coupled in QL regions. In quasi-transverse (QT) regions the coupling may be much stronger because the characteristic polarizations change rapidly with 0. The QT transitional frequency is given by j4. = 1017 NSB3, and the modes are weakly or strongly coupled according to whether f4 «f4t or J4 »jt. Estimates of ft are on the order of tens of megacycles (ionosphere) and cps (interstellar and interplanetary regions). A circularly polarized wave has its sense of rotation reversed when propagating through a QT region, provided that the coupling is weak there. If the coupling is strong, the polarization is constant across the QT region. This mechanism might explain the commonly observed polarization reversal for the wide-band solar microwave bursts. This wide-band radiation propagates through a QT region above a sunspot, and at the earth the sense of rotation reverses at the QT transitional frequency. Tbe possibility that the ionosphere and the interplanetary gas can interfere with the sense of rotation of solar radio bursts is also examined, in terms of coupling in the QT regions. Some other special situations that might arise in QT regions are briefly considered. These include the production of linear polarization, effects on differential absorption of the two magnetoionic modes, and differences in polarization that might result when either the source or the observer is in the QT region.