The photoproduction of η-mesons off ¹²C, ⁴⁰Ca, ⁹³Nb, and ^natPb nuclei has been measured with a tagged photon beam with energies between 0.6 and 2.2GeV. The experiment was performed at the Bonn ELSA accelerator with the combined setup of the Crystal Barrel and TAPS calorimeters. It aimed at the n-medium properties of the S₁₁(1535) nucleon resonance and the study of the absorption properties of nuclear matter for η-mesons. Careful consideration was given to contributions from ηπ final states and secondary production mechanisms of η-mesons, e.g. from inelastic πN reactions of intermediate pions. The analysis of the mass number scaling shows that the nuclear absorption cross-section σN_η for η-mesons is constant over a wide range of the η momentum. The comparison of the excitation functions to data off the deuteron and to calculations in the framework of a BUU model show no unexplained in-medium modifications of the S₁₁(1535).