  A model for $\pi$N scattering and $\eta$-meson production in the S$_{11}$
channel is presented. The model includes $\pi$N-scattering Born terms as well
as the N$^*${} resonances S$_{11}$(1535) and S$_{11}$(1610). The $T$-matrix is
computed in the $K$-matrix approximation. The parameters of the model are
determined by fitting the elastic $\pi$N-scattering $T$-matrix to empirical
data. We find an excellent fit for all energies up to $\sqrt{s}$ = 1.75 GeV.
Furthermore, a good description of the cross section for $\pi^- + p \rightarrow
\eta + n$ is obtained without further adjustment of parameters.
