The problem of the amplification of surface magnetic waves in transversely magnetized ferrite slabs has been solved in a general planar layered structure. It is found that the amplification indeed exists, but it is confined to a definite (very narrow) frequency range, which depends essentially on the drift velocity of the interacting charge carriers. The amplification depends in a fundamental way on semiconductor conductivity, and also on the magnetic losses of the ferrite. The above results are deemed to constitute all the essential characteristics of the amplification phenomenon. Complex-wave-number magnetostatic (ms) modes in the transversely magnetized slab are also found that complete the already-known real-wave-number ms surface wave. Consideration of these modes is required when performing the exact analysis of the amplification process by numerical computation.