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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 productionof an $\eta$-meson by a $\Delta$-resonance moving in nuclear matter. The resultis compared to prescriptions in BUU-calculations in which \et-productionproceeds both through a direct channel and through the sequential process$\Delta \to N \pi ; \pi N \to N \eta$.Comment: revised version: large parts have been rewritten, there are two new  figures. A discusion of effects of multi-body reactions of the intermediate  pion on our results has been adde

Production of eta-mesons in collisions of nucleons and delta-resonances