The specific anion adsorption of chloride and sulfate on Cu(111) from acidic aqueous electrolytes has been studied using scanning tunneling microscopy (STM) and cyclic voltammetry. At positive potentials adsorbed chloride forms a well ordered (root 3 x root 3)R30 degrees superstructure; at negative potentials the bare copper surface can be imaged with atomic resolution. By use of a so-called potentiodynamic STM measurement it is possible to correlate directly the appearance and the disappearance of the chloride superstructure to the anodic and the cathodic peak in the cyclic voltammogram. The chloride adsorbate influences the surface topography strongly in such a way that copper steps preferentially run along close packed chloride rows after chloride adsorption. An enhanced surface mobility caused by the chloride adsorbate leads to an 'electrochemical annealing' effect. Surface defects such as pits heal rapidly and the decay of copper stacks is promoted. Although the cyclic voltammograms of Cu(111) in chloride acid electrolyte and in sulfuric acid electrolyte are similar, both showing characteristic adsorption and desorption peaks, the surface structures and the adsorption kinetics are extremely different. At positive potentials the sulfate adsorbate forms an anisotropic Moire structure which occurs in three rotational domains. High resolution STM images reveal an additional species which is assigned to coadsorbed water molecules. Close packed sulfate rows are separated by zig-zag chains of these water molecules. The short range lattice vectors of the sulfate structure are similar to those found for sulfate adlayers on other fcc(111) surfaces (Au, Pt, Rh). Due to a strong kinetic hindrance it is possible to observe directly the mechanism of the sulfate adlayer formation and the decay process. The Moire formation starts locally at upper step edges and spreads from the step edges over the upper terraces. During the adlayer formation process a mass transport out of the top copper layer takes place, resulting in a drastic change of the surface topography due to the formation of characteristically shaped islands and step edges. Different models are discussed explaining the long range periodicity of the Moire pattern and the topographic changes during the adlayer formation and decay processes.