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 $Wapprox 1665$ MeV and FWHM $Gammaapprox 25$ MeV. The data are compared to the results of different models.
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