  We calculate the cross section for the production of $\eta$-mesons via
\mbox{$\Delta N \to N N \eta$} in a relativistic One-Boson-Exchange-Model.
Using this cross section we then determine the probability for the production
of an $\eta$-meson by a $\Delta$-resonance moving in nuclear matter. The result
is compared to prescriptions in BUU-calculations in which \et-production
proceeds both through a direct channel and through the sequential process
$\Delta \to N \pi ; \pi N \to N \eta$.

Nuclear Theory