Ordered structures have been observed by STM over a wide potential range for sulphate adsorbed on a Cu(111) electrode from aqueous acidic media. The structures observed are complex having large unit cells and showing both short-range and long-range periodicity, with Moire pattern formation. The short-range periodicity gives rise to a parallelogram sub-structure of dimensions b = (0.70 +/- 0.03) nm, b＇ = (0.47 +/- 0.03) nm and beta = (72 +/- 5)degrees. Three 120 degrees rotational domains are seen for this structure. This sub-structure has dimensions similar to the unit cell for the (root 3a x root 7a) structure, which has been previously observed for sulphate adsorbed on Au(111), Rh(111) and Pt(111). We propose that the sub-structure observed on Cu(111) arises also from an adsorbed sulphate ad-layer, with co-adsorbed water or cations, similar to that observed on the other metals. However, by contrast, we observe a distinct Moire pattern for sulphate/Cu(111), while no such Moire pattern has been observed for the sulphate/Rh(111) or Au(111) or Pt(111) systems. The measured ＇lattice＇ constants for the Moire pattern, which has a distorted hexagonal structure, are c = (2.9 +/- 0.3) nm, c＇ = (3.7 +/- 0.3) nm and chi = (57 +/- 5)degrees. The Moire pattern arises from the superposition of the incommensurate adsorbate superstructure with the underlying copper substrate, which itself may also be reconstructed in the presence of the adsorbate. The fact that a complex incommensurate ad-layer is formed, which does not appear to lie along any high symmetry directions of the Cu(111) substrate, indicates that strong adsorbate-adsorbate interactions override the substrate-adsorbate interactions. This gives further credence to the model in which the very similar (root 3a x root 7a) structures previously observed on Au(111), Rh(111) and Pt(111) incorporate ＇structured water＇, which hydrogen bonds with adjacent sulphate chains, forming a particular stable ad-layer structure.