[en] By use of vector eigenfunction expansion, an asymptotic nonlinear theory of a weakly ionized plasma in a strong magnetic field is presented. When the external field H is slightly larger than the critical magnetic field H/sub c/, an instability exists. For slightly unstable plasma motions, a precise form of Landau's equation is obtained. The inclusion of nonlinearities gives rise to amplitude saturation. It is also shown that, with the inclusion of small aperiodic disturbances, there exists, in the interval of possible plasma motions, a sub-interval of stable plasma motions