The stability of large magnetization motions in systems with uniaxial symme
try subject to a circularly polarized radio-frequency field is analytically
studied. Instability conditions valid for arbitrary values of the amplitud
e and frequency of the driving field are derived. In the limit of small mot
ions, these conditions yield Suhl's theory of spin-wave instabilities for t
he case of ferromagnetic resonance. It is shown that the input powers capab
le of inducing spin-wave instabilities are bounded from both below and abov
e, so that large enough motions are always stable. In addition, it is demon
strated that stability of uniform motions depends on their preparation hist
ory.