In this paper, the authors have derived a general set of coupled-mode equations for wave propagation in a wave-guide partially filled with gyromagnetic medium. With these equations, they have investigated the problem of Faraday rotation in a longitudinally magnetized ferrite rod with tapering cross-sections at both ends. Additional problems, e.g., the reflection from the ferrite rod and the effect of geometrical irregularity of the rod on the Faraday rotation, have been subsequently attacked by the same coupled-mode approach. It is shown that the coupled-mode theory is admirably suitable for the important problems herein treated. It would be extremely difficult to discuss these problems with any standard method more commonly used in the study of microwave ferrites.