  The photoproduction of $\eta$-mesons off nucleons bound in $^2$H and $^3$He
has been measured in coincidence with recoil protons and recoil neutrons for
incident photon energies from threshold up to 1.4 GeV. The experiments were
performed at the Mainz MAMI accelerator, using the Glasgow tagged photon
facility. Decay photons from the $\eta\rightarrow 2\gamma$ and $\eta\rightarrow
3\pi^0$ decays and the recoil nucleons were detected with an almost $4\pi$
electromagnetic calorimeter combining the Crystal Ball and TAPS detectors. The
data from both targets are of excellent statistical quality and show a narrow
structure in the excitation function of $\gamma n\rightarrow n\eta$. The
results from the two measurements are consistent taking into account the
expected effects from nuclear Fermi motion. The best estimates for position and
intrinsic width of the structure are $W$ = (1670$\pm$5) MeV and $\Gamma$
=(30$\pm$15) MeV. For the first time precise results for the angular dependence
of this structure have been extracted.
