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Coherent photoproduction of eta-mesons off He-3, i.e. the reaction gamma He-3 -> eta He-3, has been investigated in the near-threshold region. The experiment was performed at the Glasgow tagged photon facility of the Mainz MAMI accelerator with the combined Crystal Ball - TAPS detector. Angular distributions and the total cross section were measured using the eta -> gamma gamma and eta -> 3 pi(0) -> 6 gamma decay channels. The observed extremely sharp rise of the cross section at threshold and the behavior of the angular distributions are evidence for a strong eta He-3 final state interaction, pointing to the existence of a resonant state. The search for further evidence of this state in the excitation function of pi(0)-proton back-to-back emission in the gamma He-3 -> pi(0)pX reaction revealed a very complicated structure of the background and could not support previous conclusions. (C) 2012 Elsevier B.V. All rights reserved.