One‐dimensional three‐wave models, known for stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS), are investigated. It is shown that in homogeneous systems of infinite extent the steady‐state three‐wave solution for SBS with a reflectivity less than 100% is intrinsically unstable. From a numerical solution it is concluded that nearly all stationary states decay in time and result in a state with reflectivity coefficientR=1; only the latter is linearly stable in a homogeneous plasma of infinite length. The asymptotic solutions for SBS in plasmas are calculated and the similarity in the dynamics between SBS and SRS is discussed.