Parametric interactions among plasma waves propagating along an applied dc magnetic field are examined. The driving mechanism consists of either an ac electric field impressed transversely to the applied magnetic field, or bunches of particles injected with preferential phase. The physical system is composed of a (possibly infinite) number of cold beams. The equations are linearized with the effect of the induced first‐order magnetic field included throughout. Six absolute instabilities are found to result from the coupling between two electronic modes of a cold plasma and three more result from a coupling between an electronic mode and the ion cyclotron branch. The extension to temperate plasmas is indicated. The instabilities become important in systems with high transverse velocity&ngr;0⊥, since the growth rates calculated from coupling of modes go as&ngr;0⊥/c or &ngr;0⊥2/c2. These interactions may find application to fusion and microwave devices. In particular, those with the ions may be useful as energy transfer mechanisms.