Coupled wave equations and the corresponding wave‐energy‐flow conservation law describing the fast magnetosonic and ion‐Bernstein waves are derived for minority heating in the ion‐cyclotron range of frequencies. This fourth‐order full‐wave system is subsequently reduced in order through representation by means of two, completely decoupled, second‐order systems. One is a second‐order equation for the fast wave in which the Bernstein mode is treated as a driven response. The second is coupled‐mode equations for amplitudes varying slowly under the influence of coupling, inhomogeneity, and dissipation. The coupled‐mode equations are approximately solved for both high‐field and low‐field incidence to give the transmission and mode‐conversion coefficients in closed form for arbitrary wavenumbers parallel to the magnetic field. Good agreement with fourth‐order calculations is obtained.