A weakly ionized plasma in a nonuniform magnetic field exhibits an instability analogous to the well‐known flute instability of a fully ionized plasma. The instability sets in at a critical magnetic field. When this external field is slightly increased above the critical value by the fractional amount &Dgr;, to begin with only one mode goes unstable and it grows in amplitude to a finite limiting value. Using a general theory of the nonlinear behavior derived in an accompanying paper, we evaluate the mode amplitude and frequency shift as functions of &Dgr;, as well as the corresponding enhanced particle transport. The results are first obtained in the quasilinear approximation, but it is then shown that the mode‐coupling contribution is negligible and hence that the result is generally valid for small &Dgr;.