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 $etarightarrow 2gamma$ and $etarightarrow 3pi^0$ decays and the recoil nucleons were detected with an almost $4pi$ 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 $gamma nrightarrow neta$. 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.
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