  Coherent $\eta$-meson photoproduction on the deuteron has been studied, where
the emphasis is on the relative importance of two-body contributions from
hadronic rescattering and electromagnetic meson exchange currents besides the
impulse approximation. For the elementary photoproduction amplitude a coupled
resonance model developed by Bennhold and Tanabe has been used which fits
reasonably well the experimental data. The rescattering effects are treated
within a coupled channel approach considering the intermediate excitation of
the $P_{11}(1440)$, $D_{13}(1520)$, and $S_{11}(1535)$ nucleon resonances. The
hadronic interaction between nucleon and resonances is modeled by one boson
exchange potentials, which we have considered both in the static approximation
as well as fully retarded. The sum of all considered two-body effects results
in an enhancement of the total cross section between 10 in the maximum and 25
percent closer to threshold around 680 MeV if the hadronic interaction is
treated retarded. This enhancement shows up in the differential cross sections
mainly at backward angles. It increases steadily from only a few percent at
$0^\circ$ to more than a factor two at $180^\circ$ for a photon energy of 680
MeV. Two-body effects become also significant in certain polarization
observables. Finally, no discrepancy has been found for the ratio of the
isoscalar amplitude to the proton amplitude between coherent and incoherent
$\eta$-photoproduction on the deuteron due to a nonvanishing complex and energy
dependent phase relation.
