  Precise data for quasi-free photoproduction of $\eta$ mesons off the deuteron
have been measured at the Bonn ELSA accelerator with the combined Crystal
Barrel/TAPS detector for incident photon energies up to 2.5 GeV. The
$\eta$-mesons have been detected in coincidence with recoil protons and
neutrons. Possible nuclear effects like Fermi motion and re-scattering can be
studied via a comparison of the quasi-free reaction off the bound proton to
$\eta$-production off the free proton. No significant effects beyond the
folding of the free cross section with the momentum distribution of the bound
protons have been found. These Fermi motion effects can be removed by an
analysis using the invariant mass of the $\eta$-nucleon pairs reconstructed
from the final state four-momenta of the particles. The total cross section for
quasi-free $\eta$-photoproduction off the neutron reveals even without
correction for Fermi motion a pronounced bump-like structure around 1 GeV of
incident photon energy, which is not observed for the proton. This structure is
even narrower in the invariant mass spectrum of the $\eta$-neutron pairs.
Position and width of the peak in the invariant mass spectrum are $W\approx
1665$ MeV and FWHM $\Gamma\approx 25$ MeV. The data are compared to the results
of different models.
