The propagation, both perpendicular and nearly perpendicular, of the ordinary and extraordinary mode in a cold, inhomogeneous, magnetized plasma slab containing runaway electrons is investigated. The presence of runaways together with the density inhomogeneity is found to affect the ordinary mode significantly near the electron-cyclotron frequency. The conditions of enhanced wave absorption and/or growth are obtained and discussed for a range of plasma parameters of interest in tokamak studies.