  The role of the $\eta NN$-interaction is studied in the low energy regime in
$\eta$-deuteron reactions as well as in coherent and incoherent
$\eta$-photoproduction on the deuteron using a three-body model with separable
two-body interactions. The three-body approach turns out to be quite essential
in the most important lowest partial wave. Results are presented for
differential and total cross sections as well as for the $\eta$-meson spectrum.
They differ significantly from those predicted by a simple rescattering model
in which only first-order $\eta N$- and $NN$-interactions in the final state
are considered. The major features of the experimental data of
$\eta$-photoproduction in the near-threshold region are well reproduced.
