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Using scanning tunneling microscopy at low temperatures we investigated the adsorbate system Cu(111)-Cs for various cesium coverages. At low coverages we observe a hexagonally ordered Cs adsorption layer with a mutual adsorbate distance of 1.1 nm. This distance is discussed in terms of a commensurate adsorption superstructure which is stabilized by long-range adsorbate interactions mediated by Cu(111) surface state electrons. Intermediate coverages are characterized by incommensurate superstructures which are rotated with respect to the substrate lattice. The rotation behavior at 9K follows a general trend which is consistent with models of epitaxial rotation. With increasing coverage the adsorption layers are found to rotate toward alignment with the substrate., Comment: 8 pages, 4 figures